Have you ever wanted to compute 1000!, do calculations with algebraic numbers, or compute the Galois group of a splitting field? If so, PARI/GP is the program for you!
Obtaining and installing PARI/GP
PARI/GP can be obtained from the University of Bordeaux. There are a number of options at the download page. For Windows users, the easiest one is to select the "self installing Windows binary" (5470 KB). To install PARI/GP, simply run the file you downloaded. If you have any problems, there is an extensive frequently asked questions page, part of which covers installation.
Documentation for PARI/GP
A user's manual, tutorial, and reference card should have come with the distribution. They are most likely living on your computer at (somewhere like) C:\Program Files\PARI\doc with the filenames users.pdf, tutorial.pdf and refcard.pdf respectively. If not, they can be downloaded from the PARI/GP documentation page.
The tutorial is probably the best place to get started.