What is LaTeX?
LaTeX is a document markup language. It's used in a number of academic disciplins, but usually not law. LaTeX is different from WYSIWYG editors like Microsoft Word, in that what you put in the document isn't necessarily the same as what is output. For example, if I want to italicise a word, you do it \textit{like this}. Think of it like an HTML file but for documents.
If this seems needlessly complicated to you, that's because it is. 90% of the time a WYSIWYG editor will get the job done well. Truthfully, there aren't many use cases for LaTeX unless you want to make really nice, professional looking .pdf files. There's a bit of a learning curve to it and for most people it's probably not worth learning. That's not to say there are no use cases, however, because when LaTeX is useful, it's really, really useful.
Why should I use LaTeX?
LaTeX is particularly useful for fields that require really complex mathematical equations. In my experience, it's also really useful for anything that requires a lot of citations and footnotes that you would otherwise have to input by hand. What I'm getting at is that LaTeX is perfect for legal essays and articles. Legal citations are a huge pain and no one likes writing them and keeping track of ibids and short versions; LaTeX (or, rather, the Biblatex package) makes this task much, much easier. If you see yourself writing a lot of legal essays or articles in the future, learning LaTeX will save you a lot of time in the long run. Most of my classmates in law school would complain about having to do their citations and footnotes, but I never had an issue with them thanks to LaTeX.
Actually Writing Something
Using LaTeX isn't tremendously difficult if you know how to look things up. After the initial document setup (adding your packages, setting the page size, etc.) you will, more or less, just write it as you would any other document. The key difference is that you'll also have a bibliography file to add to. There are two citation systems that will be useful: The OSCOLA package (which is on CTAN and should just work) and the (admittedly quite shoddy but gets the job done) Bluebook package (which you'll need to install manually). You should get the gist from reading the documentation of these. In short, you create bibliographic entries for everything you want to reference, and then reference it with \cite or \footcite. As a helpful tip, Google Scholar can generate citations for articles which you can copy into your .bib file.
After Writing
Now you've written your piece, you'll probably want to do something with it. If you can get away with using a .pdf, that's your easiest option as you just have to compile one. If, as most law journals require, you need it as a .docx, you'll have to take some additional steps. This took me a few hours to work out, but should only take a few minutes for you. The most consistent way I've found is to use some software called mk4ht to convert your files into an .odt, then opening that in Word and saving it a as .docx. Make sure to proof read this before sending it off, though you should be doing that anyway.