The installer should offer a manual partition configuration scheme. If you use the typical config - / and /home and tell it to use the already present swap it should do fine. It won't overwrite the Ubuntu partitions unless you tell it to.
If you have Ubuntu latest, it uses GRUBII, which GRUB in Pardus may not pick up (sometimes it does). Just add the Ubuntu partiton to GRUB later or use the Live CD for Ubuntu to reinstall GRUBII with a line in the config for Pardus.
You can read up here - http://members.iinet.net/~herman546/index.html
- although I don't agree with Herman about "great" for GRUBII. Beta software should have no place in a final release.
Just plan ahead your partition scheme, take the install slow and don't panic. Pardus willl boot at least from GRUB, and then you can make adjustments.