It would help to further know what he/she means by "tune up".
You could run the various system clean-up jobs via tools like OnyX etc, rebuild the quick launch database, clean caches etc. That's what I could think of
Any links to any of these processes?
I assume OnyX is a program you pay for?
1. When should one use DiskWarrior?
2. How do I partition a hard drive without formatting it and reinstalling the OS?
I use it when I suspect a problem and about once every two months when there is no problem. I found the rebuild goes the quickest in Disk Warrior when you boot from another bootable disk. So if you make a clone of one OS X (bootable) with DiskWarrior on it, plug it it to the Mac you want to rebuild but have that Mac boot from the cloned firewire drive.
I never had tried iPartition but there are reviews on the net.
And how would I make a clone of OS X with Diskwarrior on it?