For more information, you can read TLDP Partition HOWTO, especially this page:
http://www.tldp.org/HOWTO/Partition/partition-4.html
For a start you need at least 2 partitions:
1 to be mounted at /
1 as a swap (allocate around 1GB? Depends on your RAM and your workloads. As a guide, 2 x physical RAM will do, although I'm a bit of memory freak and put 3 x RAM)
Now that will get your computer going. You can have other partition on /home and /usr. /home is the location of all your personal user files, so if you save a lot of video, you might want a huge /home. /usr is for all the programs, so it will depend on the amount of program. My suggestion for now is
partition at / : 7GB (this includes /usr already)
partition for swap : 1.5GB
partition at /home : the rest of the drive
So you got 3 partitions in total. =)