I found using an old credit card the best tool for removing the back cover on the Motorola Droid 3. Place the corner of the credit card in the slot at the top of the phone, continue sliding the card in, and push or pull outward. Once inserted, you can continue to slide in the card, twist it, and the cover pops right off. If you just want to use the card to get the cover started, slip it in and then you can get your fingernail into the slot. But don't bother using your fingernail, it was incredible how quickly the back popped off when using a credit card.
To replace the cover, slip the two little tabs at the bottom of the cover into their slots and snap the top of the back into place.
I really tried several times using my fingernail to get the back off, but didn't have any luck. The credit card worked like a champ.
As a final note, it really doesn't hurt the credit card at all to use it this way, but your mileage may vary.