[Galaxy Tab 10.1 Q&A, Help & Troubleshooting] krispijn_s:
I just replaced my wife tab's screen a week or so ago. Note that this is a P7510. I ordered my replacement unit from ebay ( link ). They even threw in some tools (such as the plastic triangle you'll need). How kind :)

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Definitely broken​

Before you start: WEAR LATEX GLOVES! Shattered screen is shattered, so bits of glass might get onto your hands or worse: cut you.

You have to seperate the screen/unit from the backcover with a plastic triangle or plectrum. Then carefully detach the flatcable and I'd recommend pulling out the battery plug as well to prevent the unit from turning on while you work on it.

Here's a pic of where the two connectors are located on the back of the device (click for larger!):

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Here is a vid that'll give you some reference to what you'll be doing. It also shows how the battery plug and digitizer connector can be unplugged. Vid here

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Knife totally necessary​

Then remove the screen by either carefully cutting through the glue (that's what I did; be very very patient) or by heating the bezel with a heat gun (not tested, but saw this in a repair vid). As you can see from the image above, I used a dull knife for this which I kept pointed away from the device and sort-of into the back of the glass plate. Stay away from the LCD underneath the glass: it's a very soft surface and you can damage it if you're not careful with your sharp object of choice.

Keep a vacuumcleaner handy; there might be a lot of little glass shards coming of the tab. You also might want to do this operation in a box of some sort to collect all the glass coming of.

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Face off!!​

Then patiently remove excess glue. Don't worry about buying double sided tape: the replacement digitizer has an adhesive layer on the back.

Before you put the new screen on: this is THE time to wipe the LCD clean. Most likely there will be dust and fingerprints on it. Wipe it clean because it will be locked under the new glassplate when you're done. This might also be the moment to stop and marvel at the pretty internals of the device :)

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After that it's just a matter of properly aligning the screen (note the camera holes!) and carefully lowering it onto the unit, making sure it's straight. I used my fingers as guides to make sure all edges were aligned.

If it is properly alligned, press down on the bezel and it should be fixed to your Tab. Flip the unit over and reattach the digitizer flatcable and then the batteryplug. Finally, pop on the back cover again and make sure it snaps into place all around. When I did this, the rubber seal of the microphone (next to the connector at the bottom of the device; in the pic I posted somewhat on the left where that white sticker ends) came loose. I noticed this and just pressed it back on; be sure to check this before you snap the backcover onto the device.

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And you're done!!! Good as new. Also it is now my Tab :)

DISCLAIMER: I'm not an electronics repairman, just someone who's stupid enough to just go at it. I might've done some big no-no's (like the knife), but the result is pretty good looking. You should be able to do this if you have a reasonable steady hand and patience.