HOW TO JAILBREAK THE IPAD 1st Gen
1. Review your firmware version by going to Settings> General> About and check your Version
2. If it is 5.0.1 or lower, do not update and continue to step 3.
If your version is 5.1 there is currently no untethered jailbreak available. This means you will have to run redsn0w every time you restart your device. If you don't mind, download the 5.1 firmware from here and continue to step 3. If you do mind, follow us on twitter and we will post as soon as an untethered jailbreak gets released for 5.1.
Here are the rest of the firmware links for this device if you wish to use them. (experienced users only)
3. Download redsn0w for your operating system.
4. Follow the instructions in the video below to jailbreak your iPad (for both Windows and Mac). The first video is for iOS 5.0.1 plus any lower firmwares and the bottom one if for 5.1 specifically.