Congrads on your successful research! It is a big deal. Now it's time to squeeze the most out of it...
Talk to your PI about what conference(s) it would be best at. Also consider student conferences/competitions if possible. And consider local/regional conferences (your med school may have a research day, perhaps). The AMA has a student abstract or poster competition (I think), and I know the American College of Physicians runs a competition as well, typically locally and nationally. All else being equal, I think it looks better if you show at a national non-student venue, but anything is better than nothing and winning a national student competition is pretty cool
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The bigger conferences typically have you submit an abstract and it will either a)get laughed at (unlikely if you're publishing it, unless you submit it to a totally inappropriate conference), b)invited for a poster presentation, or c)invited for an oral presentation. Oral presentations are more prestigious than poster presentations.
For poster presentations, you make up a poster (your PI should be able to help with a template, typically done as a single large PowerPoint slide then printed out at a University printing shop) and hang it when and where the conference administrators tell you to. There is usually a specified time in which you are required to stand in front of it, and people will wonder by and ask questions. In my experience 90% of the people look at the title, realize there aren't any cool pictures, and wander off. 10% will read a little bit, and maybe 1% will ask a question or two or ask you to "lead them through it". "Leading them through it" is a canned 1-3 minute talk hitting the highlights. If there's a competition involved a judge or two will come by and you'll give your talk and answer any questions. In my experience, probably 50% of the questions are pretty worthless and show total ignorance about the topic. But if it's a big conference you'll probably get to talk to the few people who are doing similar stuff and care, and that's what your PI is probably referring to about "getting some publicity." Unless you're doing a huge RCT and he is talking about press conferences and such.
I recommend showing your stuff as frequently as you can, as there is definitely an art to presenting your research in an accessible way, and practice makes perfect.
Happy to answer any other questions from my modest experience.
