The first thing to do is to sign up for a Dropbox account, which is free. The basic account gives you 2 gbs, and you get extra space if you use a referral link. Use your academic email account to maximize referral credits if you have one. The best way to use Dropbox is to put your project files in it and install the client on all your computers, or use the web interface to work on your files by downloading them to the client machine. The changes will be propagated across all your machines. It's also great for collaborating. The amazing thing about Dropbox is that it provides basic version control on your files. That is, deleted files or even previous versions of your files are automatically backed up to the cloud for 30 days! You don't have to learn any crazy version control system. It's automatic. Now I know a lot of people like to bend Dropbox into something it's not, by using symlinks to add virtual folders. Be forewarned. This can lead to problems if you have a lot of files that are changing often. Your Dropbox client may become unstable and use a huge amount of CPU. Dropbox is great, but stick with the one folder.
So there you have an amazing three pronged approach to backing up, syncing and keeping your most important files in order across machines and platforms, even if you sometimes lack an internet connection to do so. The coolest part is that you also get basic version control for free automatically. No need to struggle with Git or Subversion. What solutions are you using to keep your files in sync across machines?