On getting published in the research field

A few weeks ago I had a meeting with my current PI and as we were going through the agenda (who should send out which emails, documents that needed to be updated etc.) she casually drops this bomb: "oh by the way, you should probably get started on drafting the manuscript for Aim 1." I know this is an incredibly cliche phrase to use but you LITERALLY could have heard a pin drop. I actually didn't know how to respond so I just nodded, mutely. On the one hand I was THRILLED (excitement level: mentally jumping up and down) and on the other I was terrified because I've never actually written a research paper on my own before, at least not one based on scientific data. Also I've only been on this project for three months! Thankfully my PI went on to explain how she was giving this to me because she has been very impressed with my involvement in the study so far and really wants me to have a publication before I leave (which may or may not be in September but that is still very up in the air). It calmed me down somewhat to know that she has a lot of faith in my abilities and clearly wouldn't be giving me this task if she didn't think I was up for it.
While I've been incredibly lucky and am thankful to have been given several opportunities to get published before applying med school, I don't necessarily think it's completely up to chance. There are definitely things that anyone can do to help get their name on a paper they can include in their resume, CV, or grad school applications.
Probably the most helpful thing you can do for yourself is be proactive. I kind of hate that word because I think it's overused but it works in this case because it means "creating or controlling a situation by causing something to happen" (Google) and that's exactly what you want to do. If you already work in research and you want to get your name on a paper, don't just wait to be approached, talk to your PI about wanting to take on more responsibility and ask about the possibility of being included on a future publication. The worst thing they can say is no and you're no worse off than you were before. You can also talk to fellow RAs and ask if they need any help on their projects that may give you credit. Sometimes this might be tricky to navigate because I know some places are more competitive than others but in my experience I've found that any help offered is often gladly taken and you'll at least get a mention for it.
If you don't already work in research but would like to, start asking around because a lot of RA jobs are filled through recommendations (that's how I got my position). If you feel like you aren't close enough to the people you would ask just do it anyway. We've been looking for someone for our FDA project for months and if my roommate's sister's best friend contacted me asking about working at Partners I'd probably recommend her to HR as long as she wasn't a huge disaster (side note: we're still looking for someone for that project so if you're interested, holla at me).
If you're worried you won't get hired due to lack of experience then stop stressing because you're probably awesome in plenty of other ways. I've talked to several coworkers who have conducted interviews lately and was told that they primarily look for someone who is independent, goal-oriented and willing to learn. What you already know matters a lot less than how hard you work to get better at new things. Also doing all the regular things like showing up on time, not being rude, and dressing nicely really help (seriously, some interviewees don't do this, it's crazy).
Above all else, persevere! I guess it's mostly common sense but if you don't get the first job you interview for or your query about being on a paper is shut down then just keep trying. You'll get there, I promise.