(Made up character) Farrel jumps from his rambler house roof but lands horizontally and on his left arm. His left arms ulna snaps and pierces out of his skin. This is just an example because I'm having trouble with my real story (where the main character gets impaled on rebar) but having trouble explaining it in first person.
Welcome to the site, Bruce!
In this case, describing pain in the first is no different than doing it in the third person. The only difference would be that you would use 'I' rather than third person pronouns.
Therefore, what it looks like you're really after is how to describe pain in general. As far as being impaled on re-bar goes... well, I think we can scratch first-person accounts of how it felt. What you need to do is imagine how it would feel, and write that down, ignoring how it sounds at first.
Once the idea is there, go back and rewrite it, describing it using adjectives, adverbs, and verbs that compliment the experience. You want your reader to feel the pain the way your character does. For example:
Farrel's forward momentum came to an abrupt halt as he slammed into the re-bar. He felt the rough metal slice through his body, plunging through organs, ripping through skin, and shattering bones. A second later his face collided with the hard concrete the re-bar was buried in, smashing his nose. He could feel the vibration of it shudder all the way through his body, which only made the pain ten times worse.
Note the descriptive verbs I use: slammed, plunging, ripping, shattering, collided, etc. I wouldn't, for example, use such words as arrive, land, connect, etc. because they aren't as vivid. The words I used help to convey the feeling of the pain to the reader.
Hopefully this is what you were looking for.
The writing of this passage depends on what you intend to underline; is the character under a lot of stress or would he rather describe the scene factually, as though detached from what he's experiencing ?
If the scene intends to underline the horror of the moment, stick as closely as you can to what the character might be thinking/feeling at the time; at this level of pain, perception dwindles down to the most basic form of sensation :
Searing pain, and my vision goes blind. I can't breathe. I can't move, and my head is spinning, threatening to shut down althogether. (...)
If you intend to focus on what happens next, a more detached approach might be useful.
I looked down. There was a rebar sticking out of my stomach.
And then move on directly, as though it were just an offhand comment. On many occasions characters (as well as real people) don't react to trauma the 'natural' way; it's an interesting thing to play on, especially since you're writing in first person.
I agree with Tommy in that visualization is key in describing anything from a first person point of view. He was also correct with the words: it's all about the adjectives and adverbs you choose to use. Some other good ones to describe pain are surging, tearing, wracking, burning, smoldering, piercing, unbearable, searing, etc. If you want to really give depth to the pain, getting pretty graphic with some specifics as to what's going on is also a great idea, as long as it's not so much detail that it becomes tedious. Using first person is also great in situations like this because it allows you to go much deeper into the thought process of that person. A simple way to think of it is "what would be going through my mind if this was happening to me?"
Example for the scene:
The bone snapped with a crack so loud it echoed through the silence of the night. My head spun violently, and looking back, I could see white bone gouging out from the bloodied mess that was my arm. For some reason, my brain refused to believe it. Everything was spinning by now, spiraling into a black nothingness, until...
I often describe the reaction to the pain and the action causing the pain more than the pain itself. You can say that it's agony, anguish, a tribulation, but it won't have an impact unless you focus specifically on what causes it.
Focus on the sound of the words. Surge, gouge, sear, smolder, snap, plunge, slice, saw, splatter. I would also use thrust, but that has a completely different meaning that you probably don't want to touch here. You don't want passive words, you want words with a connotation of destruction. This type of pain won't be silent, either, and immediately extreme pain probably won't register. Describe the wet crunch and then the surge of pain as 'your' bone plunges through flesh. 'You' grapple for the injury (people hold onto broken limbs somewhat instinctively) and blood splatters all over 'you', smearing when 'you' try to stop it. 'You' strangle a cry in 'your' throat when the limb shifts unnaturally under 'your' desperate grip, pain slicing through twitching, torn muscles.
For me, there was an uncanny valley effect. When I broke my arm, I didn't feel pain until I looked down at my two wrists, where there was only supposed to be one. The second 'wrist' contorted unnaturally, bent shards of bone scraping over muscles. When it started to hurt, I couldn't see anything anymore, but the pain wasn't going away after my brain registered the horror of what had happened. I'm just glad it wasn't a compound fracture.
Depending on 'your' persona, maybe add a few swear words.
Don't hurt yourself, but the next time you do, write it down, or at least think up some words for it. If you can't think of anything more than $#!%, that's okay, because your character probably won't be able to think much more than $#!% once the pain really starts.