'Do I need to root my phone to use my phone?'
Android is a very open mobile OS, you can change all aspects ranging from homescreens to keyboards just fine without any kind of root unlock. Root is required if you wish to unlock certain permissions (e.g. adjusting the CPU speed) and/or install custom ROMs.
A custom ROM is a community-made modification of the Android OS, customizing it more in some way. Additional functionality (like joining ad-hoc wifi networks) or more sleek set-up (speed, control over battery life) can be gained and in some cases stability (more bugs) or your warranty lost.
'How do I get started?'
You will need to gain root access on your device and use a ROM specifically suited for your phone model.
Check the XDA dev
forums, scroll down to the forums of your device and check out the Sticky threads. Be sure to follow them with care, backing up where they ask you to back-up your original stuff and using the right instructions for your device versions.
Rooting has its risks! Be prepared to have to tinker with your device in case shit goes wrong.
Also, before you do anything to your phone in recovery mode (you'll probably have to go there as part of the rooting process if you decide to, as well as if you are flashing any custom ROMs) make sure your battery is charged! If you're plugged in it won't charge while in recovery; this is probably the quickest way to brick your phone.
While flashing your device it's recommended not to charge the device - it may fool battery calibration a little bit (although that can be re-calibrated later).
Note that while rooted you may not be able to receive official OTA updates, or if you can - they will make you lose root. If you install a community ROM they will most likely incorporate the official update in a newer version.
There's an easy '1 button root' program called UNREVOKED
which is compatible with the following devices:
unrevoked3 currently supports the following Android phones:
Sprint EVO 4G (HTC Supersonic)
Droid Incredible (HTC Incredible)
HTC Desire GSM
HTC Desire CDMA (HTC BravoC)
Droid Eris (HTC DesireC)
HTC Wildfire (HTC Buzz)
All you need to do is make sure your drivers are set-up (USB debugging for Android) and then run the app. Windows users need to install hboot drivers as well.
There's a guide available
that goes through the driver steps for the HTC Desire (likely similar for the other devices).
The ADB driver for HTC phones is usually included in HTC Sync (but make sure HTC Sync app itself is uninstalled before running unrevoked).
Recommended root apps:
(free version can also be found on XDA)