How to make and restore a Nandroid Backup

Here's a quick little guide about how to make and restore from a Nandroid backup:


Backup

1. Download Rom Manager from the Android Market (Market Link  - Price: free)
2. Open Rom Manager and choose "Flash Clockwork Recovery". Rom manager will download a recovery image for your device (this recovery image is needed so Rom Manager can restore from a nandroid backup you make).
3. Once the Recovery image flash is ready choose Backup Current Rom. This will make a complete backup of the system files and your installed programs and data. (The system will reboot itself to make a backup and reboot itself back if it is ready. Don't interrupt this process)
4. Ready :) That's all.

Restore 

1. There are two ways to restore a backup: 1) in the Rom Manager app itself and 2) By going into restore mode. We are going to cover the 2nd option here because that's what you want to do if the device doesn't boot properly after a density change.
2. Go into recovery mode (Every device has a particular way to boot into the recovery mode. Here are some links to how it is done for some devices: Samsung Galaxy S and variants , Droid X , HTC Evo/Legend/Desire . Another method is to turn on USB Debugging on your device and do it with ADB on you PC with the command adb recovery
3. Select apply update.zip . This will start the ClockworkMod Recovery (the image we flashed in step 2 of the download guide).
4. In the ClockworkMod Recovery Menu select nandroid. 
5. Now you can restore you system by selecting Restore

 ( Extensive guide with pictures and more background info: see this article - info about supported phones is obsolete)