You don't compile scripts; you just run them. For smaller scripts I just use Gedit, Pluma or Kate (your system's default text editor, unless you are on Xfce). For bigger scripts, something like Geany might be handy though Kate will hold its own with larger scripts just fine and gives you plenty of tools and features lacking from Gedit and Pluma.
To learn about scripts, assuming you mean shell scripts, you just have to learn about your command shell (the thingy doing for you what you type on the terminal). The default shell on Linux Mint is Bash (yes, as with anything else on Linux you have a lot of choice and can use a different shell). To learn about it, I'd recommend this guide: http://flossmanuals.net/command-line/
. Also downloadable as a free ebook or you can buy it printed.
There are many scripting languages you can use on Linux in addition to shell scripting. Things like Python and Perl, which also don't require compilation either (being scripting languages).