As Yancek says, Puppy is not really intended for very small computers. Even if you put it on a HD, the usual method is what they call a frugal install, where it still loads into RAM to run. You can do a conventional install, but the result is not secure
, which why they don't recommend it.
There are several distros which will be happy with 198MB, but AntiX is the smallest. Last time I tried it, it idled in less than 60MB and ran a web browser in 120.
Get the full version of AntiX 13.
Your live CD of AntiX will come with a program called GParted, which you use to set up your hard disk before running the installer. This is the best tutorial:
You should end up with four partitions:
sda1: where XP is (defrag in Windows, then shrink it a bit with GParted)
sda2: where Linux goes (3 GB)
sda3: for swap, used when you run short on memory (about 1/4 GB)
sda4: for /home, where your own files go (as much as is left)