Here are the step by step instructions on how to flash the Galaxy Tab 10.1 Jelly Bean Android 4.1 ROM. The steps are pretty easy once you have ClockworkMod installed and even that is not too difficult.
Step 1: Install ClockworkMod recovery if you have not already.
Step 2: Download the appropriate ROM for your device under the DOWNLOADS section. Also download the latest Google Apps from the same section.
Step 3: Boot into recovery by holding the volume down key while the tablet starts up. Then press the volume down key again to toggle the selection to the left. Press volume up to select it.
Step 4: Select backup and restore and create a backup. Navigate with the volume buttons and select with power button.
Step 5: After the backup select wipe data/factory reset.
Step 6: Select wipe cache partition.
Step 7: Select advanced and Wipe Dalvik Cache.
Step 8: Select install zip from sdcard, choose zip from sdcard, and find the ROM that you downloaded.
Step 9: Then do the same thing but for the Google Apps file that you downloaded.
Reboot your tablet and hope that everything worked out. If your tablet takes more than 10 minutes to start up then something might have gone wrong. You can restore the backup you made in recovery to go back to your previous setup. If you receive a popup that asks you to accept Google Now, then decline it because it will force close.
You will also need to enable the keyboard in the settings by disabling a hardware keyboard. This will need to be done each time the tablet restarts.
To fix the keyboard, go to Settings > Language & input > Default [English (US) - Android keyboard (AOSP)] > Swtch Hardware to OFF