Sage

Go to sagemath.org and click on "Sage Via the Web".
You will need to make up a username and password.
Once you have logged in, click on "new worksheet". Type "1+1" (without the quotes, here and later in this explanation) into a cell on the worksheet, then hit Shift-Enter. If everthing goes OK, you should get "2".
Now type "plot?". After a few seconds, you should see more than you want to see about the plot function. I usually skip through the documentation looking for examples. Try plotting something.
Other keywords you might try: integrate?, diff?, solve?, limit?
Try "expand(x+y)^5" and "factor(x^2+2*x*y+y^2)".

From the Sage homepage, click on "Help". I would recommend the Quick Reference Cards, Sage for Newbies, and the Tutorial pages.

To download Sage, go to the Sage website and click on download. There is an Installation Guide available in the "Help" section of the Sage site.