Is there a way to install LaTeX onto my computer so that I can use it when I am not online?
using Eeebuntu (Ubuntu) on my netbook (eee pc) together with TeX Live 2008 and the editor Kile. If you are using Windows I agree with Chris. MiKTeX is a good choice and easy-to-use, though TeX Live is a very good alternative. TeXnicCenter would be my choice for Windows too.
Perhaps have a look at Essential software for LaTeX, choose your operating system there and have a look at the distributions, editors and viewers listed.