Since I'm only just dipping into this, I'd like to offer some, even though still very young, personal experiences.
Many students in my country get published before pursuing a PhD (I'm not one of them and have only just learned the process). They literally have a page full of publication before applying for PhD. Usually, they start to work a few years after their master or Bachelor and get involved in research projects. Once you are a part of the research then there are many opportunities for you to be a part of writing papers as well. Of course you don't get to be the first author right away, but you still have your name in the papers and you get to observe and learn from experienced writers and researchers. (I finally had the gut to ask my boss to lead a paper the other day).
As for looking for a journal. I actually finished submitting a paper a couple of weeks ago (Not my paper, but it was a task I was assigned to). What I did was 1) look at the journals that published your researchers' previous papers or papers that you read and were interested in 2) http://jane.biosemantics.org/suggestions.php offers great suggestion but not always 100% matched your interest 3) ask around for suggestions (your professors, your researchers, your friends who published, etc). After doing all that I compiled an excel list of around 10 potential journals before picking one for various reasons (publication fee, impact factor score, relevance to the paper, etc). I'm still very new to this area so looking forward to reading more about everyone's experiences.