There's a lot to like in each answer, but I want to attempt to answer this myself, both for feedback and to bring it all together into one answer.
A treatment is...
... at the highest level, a treatment is a summary which presumes the reader wants to know all of the important pieces of a story. Everything should be spoiled. This is typically used as a document for the sales process; but if one's goal is to sell a book, being able to write a treatment for said book should be one of the benchmarks used to determine if the work is "good enough".
Elements of the story that do not find their way into the treatment are potential targets for elimination. However, many elements do not belong in a treatment by necessity. What we are looking for when cutting at this level in revision are elements that are superfluous (too much of a thing), extraneous (off topic), or inconsequential (having no meaning or desired effect).
What we are looking to change at this level are things which do not serve to construct the type of story we are looking to write. A good treatment will show a steady rise in tension until we reach the primary conflict resolution. Things which distract from that graceful arc or muddy the waters ultimately need to serve some great purpose in the work to persist unchanged.
In order to assure that rise in tension, we construct a treatment out of beats.
What is a Beat?
A beat is many things to many people and has very specific meaning in staging. But, for the purpose of a treatment, a beat is a discrete element which furthers a primary consideration in your story: It is the moments of decision, characterization, conflict, etc that are the figurative struts of your novel that change its direction or reveal consequential information to the reader. An impactful beat will be one that strongly resonates with the readers emotions. For instance, a good characterization beat will make the reader feel that that person is real. (Aka, save the cat / pet the dog)
But what it ultimately is, is an explanation. It is the act of telling instead of showing. “Showing” is an act of expansion, while telling is often an act of compression in writing. You want to strip out most of the description and facets that help describe your setting and world and make it feel real and instead boil it down to exactly what happened and why. Even better if you can tie this immediately to emotional consequence. Cause and Effect. And do it succinctly for each point.
A scene is usually made out of several of these explanatory sentences, but the beat itself is the unit of sentences that leads to critical development in the understanding of the story, characters, or conflict. The number of beats per scene should not be very high, but it will vary per chapter depending on what that is accomplishing.
A beat, in these purposes, is the smallest story in your story. Which makes them easier to write: BEGINNING! MIDDLE! END! with a heavy emphasis on compact meaningful explanation.
If you are writing a treatment for the purposes of revision, then your beats need to look a bit different than they would for a sale. One, because when you are selling your book you are talking it up; but when you are revising, you're looking for both your weaknesses and your strengths. In both cases you should be honest, but there's a difference between a blue print and a fully constructed building which hides all of the mechanical details and invites someone to come inside. When the revision process is done, the treatment shouldn't be too far off from the sale-able version, and if you're looking for something to measure it's likely that the treatment itself has become a positive advocate for your story.
How to write a beat?
There aren't many articulated approaches on this, which was the main reason I asked this question. Most people who understand beats, understand them intuitively. Ask someone who plays the violin at an expert level how you, a novice, can learn to do this and you should be prepared for a lot of well intentioned abstract ideas that won't help you progress; when what you really need is a boring step by step guide to the basics.
Step 0: Outline or Reverse Outline your work; Or, look only at a specific scene; Or, if you're not a discovery writer and you're doing this on the front end, be prepared to make things up.
Step 1: Identify points of conflict at the point you are currently working on.
Each beat is going to circle around a conflict. This is either the inciting incident for your beat, a point of raised tension, or the climax right before the resolution.
Step 2: Identify the players and figure out who the "protagonist" and "antagonist" are for this beat.
Note, this could be man vs self (internal), man vs external (nature or man), but you should know what it is. This is your opening to the beat. Explain, why each opposing/conflicting force is the way it is. Then explain how this conflict interacts. Then explain how this causes a change, either in situation or understanding. The beat is resolved when the "moment" ends with the story going in a determined direction.
This should be done in 2-5 sentence. Be concise, whatever the opposite of purple is, and most importantly forget everything you learned about show. Now it's time to simply tell the reader what's going on. No mysteries.
Step 3: Making your Beats useful
Collecting all of these beats should create a concise narrative that tell the core of your story. For purposes of revision, you may wish to have a second column or track changes comment attached to each beat that has the meta data you will find relevant for revisions. The meta data (or data about data) can be helpful when you're trying to make sure you have earned your moment or it may just be word counts so that you know where your document is dense and where it is light.
Note that the beat is the story, but it is not the details. The beat is useful by telling you what the moment accomplishes in your story, while being bereft of the explicit detail involved in making that happen. This gives you the power to keep your beat, while changing your implementation. Your beat should be an abstraction.
Step 4: Choosing Your Beats
At this point you want to take all of your tools out of your tool box that help you understand narrative structure. You may also want to apply a theoretical story framework: 3 act (google: hollywood), 7 point plot (google: Dan Wells), Scene-Sequel, etc.
All of these tools are optional and should be chosen to create the pacing and effect on the reader that you think best suites and will sell your story. You now need to identify what each beat is doing in the terms you have chosen to work with:
- Raises stakes
- Characterizes someone/something
- Releases tension
- Reveals information which changes someone's understanding
- Generates an emotional response in the reader
Each beat should do something that enhances your story, but that does not mean that everything you've written down at this point is actually doing that. A weak story will often have a bunch of disconnected beats that are more like a pile of bricks than a wall.
Step 5: Make choices.
Once everything is down in front of you, you seek external input or you may be able to see for yourself exactly where your weak points are. Use this as a guide to keep your story on target and potent. When a chef makes food, they cut away that which they don't need; when they make a sauce, they boil off the water. That is what this process is about: finding your flavor and intensifying it by removing the bits that are in the way.
You have only a few choices to make at a macro level, though they'll have infinite variation once you get down into micro:
The continuum of possible revisions:
- Remove a beat that's not doing important work
- Merge multiple beats into a single more effective beat
- Minimize a beat that's not important, and is simply too "heavy"
- Leave a beat the way it is if it's working
- Re-order beats to enhance their performance
- Alter a beat so that it serves a more specific purpose
- Add in beats that are missing to strengthen the story
- Reconstruct a series of beats to hit a specific target
Step 6: Apply to Manuscript
Either write your manuscript, or if revising as I am, remove anything that correlates to beats that should have been removed. Re-order your information and connective tissue to serve your treatment. Write what is missing. Identify the information that wasn't part of a beat, and if it doesn't serve your narrative goals, remove it.
How do Beats help the revision process?
At this point it should be relatively obvious how beats help the revision process, but to state it concisely: Once you know all of the little stories that make up your story, you can make sure that all of those stories are relevant to the story you want to be telling AND the story that people want to be reading. The treatment is the map, each beat is a hash in a dashed line showing the way to your X. By writing a treatment you will have:
An understanding of your narrative strength
Once all of your beats have been listed out, you have to know what your goals are. At this point it should be relatively easy to tell what your story is about. If it’s not easy, that’s a good indicator that the beats need to be tightened up, that they don’t lead smoothly to the end.
An understanding of where you are speaking for the sake of being heard, but not developing your ideas.
If your problem is one of length, then keeping track of your word counts per beat is a really good way to figure out where you should focus your cuts. And the beat itself should help you figure out what is actually necessary in the scene, helping you get in late and out early. But, also you can tell where you are being excessively repetitive. Note, you need some repetition for things like foreshadowing, but if you do it in the same way ever time it will become repetitive for your reader; or worse, you simply won't be presenting them with novel ideas.
A map to enhance the emotional impact of your story and earn your consequences
If your problem is one of tension, then you have at your hands the entire structure of your story. So, you can figure out where you need to up the tension by raising the stakes appropriately or where you need to cut something that is throwing off the pace. On the reverse, you can also make sure that your beats are constructed in a way that makes your readers identify with your characters. This is a great way to tell if you have done the work to earn your big moments.
In "Sandersonian" words: We're going for, Surprising yet inevitable; which means your work should lay the ground work for the motivations that lead to the unexpected, but entirely believable points at which the book turns. A treatment with appropriate beats should have all of these moments and you should know where each moment is earned in your book.
An understanding of what you are good at and what you need to work on
At this point it should also be obvious where you are repeating yourself or duplicating your work; which should give you more goals for revision. If the treatment looks like a bunch of things happening instead of stacking up and developing a sequence of interesting events that compound and interact, that make you better understand your characters and their challenges, then the focus needs to be on figuring out which beats are working and trimming away the ones that don’t contribute to the story you want to tell.
Another possibility, and one I'm finding in my own work, is that my characters often do things because they "should" because external pressure and expectations have guided where I take them. But, this means they lack agency. So, I know that one of the things I need to do is work on that unique agency that makes these people feel like they are real and gives people a reason to be attached. The tell or smell for all of this is that in the beginning-middle-end my explanations for my character's movement through the conflict is often weak.
Hopefully someone else has found this answer helpful. I have learned more about this process by writing it out and combining all of your ideas and others and I have at least convinced myself this is the right thing to do during the revision/editing process. I will likely continue to work on this definition and guide as I apply this tool to my process or receive feedback. For those of you looking for a TLDR, here it is:
Beats are the smallest stories in your story, comprised of a beginning, a middle, and an end. A successful beat's climax alters the direction of the story and causes the reader to buy into the book further. Beats should be 2-5 sentences and abstract explanations of what has occurred, bereft of the the specific details that make the moments work. When combined into a very short narrative, Beats can be used to construct a treatment or summary. Once you are working with the emotional levers of your story, you can find the weak or missing points or cut the extraneous ones. At the end your manuscript will be more concise, more impactful. It will be easier to explain as well as sell.