Use Gingerbreak. Available here:
[26.04.2011][v1.2] GingerBreak APK (root for GingerBread) - xda-developers
I emailed myself the file. This is my first android phone and first rooting experience, this couldn't have been easier.
After this I installed the following applications:
Allow applications to elevate to super user rights
https://market.android.com/details?i...fou.android.su
Allows "freezing" of bloatware (recommended instead of deleting the files so over the air, OTA, updates are not affected)
https://market.android.com/details?id=com.bloatfreezer