I have always struggled with writing dialogue between my characters in my historical fiction novel. So, when it is possible to avoid dialogue, I avoid it. In the scenario I am writing, I have 2 characters who are meeting each other for the first time. Obviously, I need to have some dialogue, as there is no other way to formally introduce 2 characters. A dialogue rule I am aware of is that the dialogue must move the story along - no small talk. How can I have these 2 characters meet for the first time and have no small talk but it still seem realistic? I want the minimal amount of dialogue for this, but make it still seem realistic and move the story along. How can I accomplish this?
Before you read this answer, do something first; I want to find that rule book that says no small talk, set it on the ground outside, light it on fire, shoot it half a dozen times, and then put whatever is left in the garbage can. Done? Good. Continue reading.
Besides grammar and spelling and general formatting rules that your English teacher probably taught you, 'rules' are just practices or strategies that somebody decided worked well for them. What worked well for somebody writing story X won't work the same for your story Y. I used to not use much small talk in some of my stories, and they ended up being rather bland and not all that interesting. Now I'm trying to change that, and the result is a lot better than before. One other thing I want to point out is that if your story is all 'run run run run run' between plot points, it's a really quick novel. Good for convincing people not to put it down, but it will get rather repetitive.
In answer to your question;
To have no small talk, just have them talk about important stuff like the back story of how they got there and whatever else will come into your story later. This is called the Chekhov's Gun principle, which I personally think isn't a very good idea because you really have to strip your story down to just the big things.
In answer to what I think you should be asking; How to write a good first encounter?
Take the opportunity to slow down, your characters are meeting for the first time. First impressions mean quite a bit, in writing and in real life. If you go with the no small talk option you seem to want to go with, then all your characters will end up sounding like single minded robots only trying to accomplish whatever it is they set out to do. Although robots would probably just attach a USB cable and download the information, but you get the idea. Anyway, back to the encounter. Depending on what the POV is, it will vary how you go through this next bit but it's pretty interchangeable for whatever POV you use.
Describe the person(s). Before you talk to someone, you probably see them(if not then skip to #2). Spend a bit on describing the character you are encountering, if your in the middle of a firefight then keep it short, maybe just a quick sentence. If nothing important is going on, maybe do a whole paragraph.
Start the conversation. Go ahead, get friendly and talk about whatever you think the characters will find important. This will also be the place where you have to describe their voice if it's the first time. Maybe they have a cold, or are dehydrated, which might make them sound a bit different than they normally would.
Keep talking. Once you get the conversation going, it can be hard to stop. Go ahead and just write it all out, or at least until the evil guys find them and they have to run away. Probably you'll have something else besides just talking to sprinkle around the dialogue. If not, thats fine to. Is one of them sick? Do they need some food or water? Medical attention for their injuries?
End the conversation and continue with the story. Since you don't seem to like writing dialogue, then this should be an easy step for you. Once you've gotten all the important stuff done and finished a decent amount of small talk, then you can finish bandaging that wound/feeding them/finding the medicine and continue with the plot.
Hope this helps, good luck!
The answers above are both good, so I'm just adding a few extra notes:
It depends how important each character is to the plot and to the other character how much time and detail you should put into their first meeting. It also depends on whether or not you are simultaneously introducing the reader to these characters as well as introducing them to one another.
What is the minimal amount of dialogue you could use to introduce two people? The answer is none. There are situations and context where you could get away with no in text dialogue at all, something like this:
Alice hadn't waited long when someone who fit Nathaniel's description entered. Sure enough, he headed in her direction, no doubt recognizing her as well from what Sally had told him. She smiled, hoping it didn't look too awkward, and they exchanged pleasantries, waiting for Sally to arrive. She learned he was a journalist, which she hadn't known, and he seemed genuinely interested in her work studying marine life. He also had warm brown eyes and a quick smile, and Sally found herself relaxing and enjoying his company, despite her earlier apprehension. They were discussing a recent news article on platypuses when Sally finally rushed in, looking out of breath and excited.
Edit: though your situation, as described in the comments, doesn't sound like one where you could get away without dialogue! It sounds like what needs to be discussed is pretty important! As the others said, think about what each character's motives are, what questions they will want answered, and so on. And go from there.
Be true to your characters. Your question is a challenge only if both of your characters are people of few words.
In any kind of situation, when two people meet, there is something that they would want to say to each other. In your particular situation (disclosed in your comments) I believe those two have a lot to say, if they are in any condition to talk.
So, spin out your dialogue based on how it might go. Then return to your writing and prune parts of it that seem excessive. And also, small talk may not advance the plot, but it does serve the purpose of character development.