Overleaf is quite easy to use if you don't mind needing to be online to work. It lets you edit your project in a browser, and their server has a full LaTeX installation, so there's very little setup required. It is also a great way to collaborate on papers.
Alternatively, the Linux computers in the basement of Kemper have LaTeX installed already. If you want to use your own computer, you'll need to install it. Different operating systems have different popular LaTeX distributions:
In each case I suggest installing the full version with all packages.
Once installed, you should be able to create a PDF file by doing the following:
This should produce the file sample.pdf. Sometimes you have to run it twice to get all the references correct.
Comparing the source code in the file sample.tex with the output it produces in sample.pdf is a good way to learn some simple LaTeX techniques by example.
Search engines and the course online discussion forum are useful if you can't find something you want in the example file. Here is a list of several useful symbols.
Learning LaTeX is like learning a programming language. That means do the same thing you'd do while programming: start with a simple file that compiles and make incremental changes, compiling often to ensure you haven't introduced an error. If you type for a long time and only then try to compile, then it may require a long time to fix all the errors. Instead, compile often and fix each error as it appears.
There are editors that make editing LaTeX much easier.
An alternative available on all three operating systems is TexStudio, but I haven't used it.
What I've found very useful from WinEdt when I was learning LaTeX (some other editors have this as well) is the visual menus that make it easy to look up LaTeX code for math symbols, which can be faster than searching the internet.
On any of these editors, be sure to set it up to use pdflatex to compile. The program latex outputs a DVI file, which can be converted to PDF by running the program dvipdf, but the simplest thing is to run pdflatex, which directly creates a PDF file.
To create figures such as drawings of finite automata, there are a few alternatives