There really isn't too much you can do.
Firstly, I would surf Firefox in privacy mode (assuming you have a FF installed that will support this). If that wasn't possible, try using a portable firefox on a USB stick or some such.
I would also agree to using Truecrypt. You can create a file container with it and use that as a small portable filesystem.
Those are the two best things you can do since the biggest reasons you would have to use a computer in a lab (w/o admin rights) is as a student. I'm assuming your use case is projects and surfing the Internet. You can store any projects that you're working on in Truecrypt and it will only be available to theft (at least easily) and such while you have it open and are working on it. The only way to escape someone stealing online credentials would be use either a portable web browser in an exncrypted Truecrypt container or use a web browser that doesn't save credentials, cookies, history, etc.
Other than that, without being an admin you are extremely limited in options. On top of the above, use safe habits, assume the admin has access to any/all of your files whenever he pleases, and assume your network traffic is always being monitored.
EDIT: This has some useful information for you on the Truecrypt end. It's a thread where someone has the same issue as you. One person in there recommended running things from a USB device that has HW encryption to avoid any privilege issues.