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.
http://antix.mepis.org/index.php?title=Main_Page
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:
http://www.dedoimedo.com/computers/gparted.html
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)