This thread is going to be a sticky thread that we'll modify over time to cover all the problems that might happen while installing Windows XP on your new Windows Vista machine.
For an overview of the steps required to shrink your partition and run XP and Vista in a dual-boot configuration, you'll first want to check out this article:
Install Windows XP on Your Pre-Installed Windows Vista Computer
If you have problems shrinking your Vista partition using Disk Management, you can read this article to understand the problem:
Working Around Windows Vista's "Shrink Volume" Inadequacy Problems
And then read this article that covers another workaround using gparted live cd:
Using GParted to Resize Your Windows Vista Partition
Troubleshooting XP Install
For problems with Windows XP installation:
Resolving "Setup did not find any hard disk drives" during Windows XP Installation
User-Contributed Guides (very useful!)
Dual boot XP and Vista on the HP dv2550se "Verve"
If you can think of anything else that should be in this list, post a response and we'll add it.