If you do 'df -h' from the command prompt, it will tell you what disk partitions you have, and how much space (in Kb or Mb or whatever) is available on each one.
You can resize and move some types of partitions, and 'parted' seems a pretty good tool for this. If you can shrink one partition a little, or find some unused space, you *may* be able to increase the size of the patition you want to grow. You'll need to have the space you're extending into located after the partition you're growing.
What you want to do is difficult and dangerous but not impossible. Please make sure you have a readable backup of important stuff before you begin, or else try it out first on a test system.
As mentioned elsewhere, grab the latest source for parted, and use the 'mkparted' script to help create a boot and working floppy.