There is no "best" way, other than needing a seperate partition for each distro. The good news is that it's very simple, and actually difficult to screw anything up.
I'm assuming there's no Windows installed, since you didn't mention it. This really only affects your bootloader setup.
If you have freespace, just install your new distro on the spare partition (logical is preferable). You can either reinstall whatever bootloader you're using now --grub or lilo, presumably-- to get the new entry, or else skip the booloader config during install and add it manually afterwards.
If you parititoned your whole drive and don't have any freespace, you'll want to repartition using Partition Magic (my preference, but costs $$$) or an open source clone like qtparted (never tried but heard good things). Of course, back up any critical data before mucking around with repartitioning.
You do NOT need a seperate swap partition for each distro, btw... use your existing one when installing your new OS.
Hope that helps. Good luck.
EDIT - Partition Magic, not Partition Manager. doh!