I posted a clip on YouTube removing the back from the RAZR.
Its really not that hard. Only tools I used were my fingers.
Sent from my DROID RAZR using DroidForums
I second that.
I did discover the proper way to remove the back cover without doing any damage. First, you either need a spudger or other semi-rigid plastic tool (like perhaps a plastic knife), or you can use your fingernail if it's stiff enough. For me, the fingernail worked fine.
Starting from the bottom right corner (when looking at the front of the phone), carefully but firmly work your "tool" into the thin opening between the back cover and the black rubberized rib that runs the entire circumference of the phone. If you are careful but committed, you will feel the bottom corner give way and "pop". Once you have that corner loose, you can then run your "tool" (i.e. fingernail), up along that side of the phone. The nubs that hold the cover onto the frame are on the back cover and fit into small indentations in the phone. By gently prying the back cover edge out and toward the back of the phone, you'll progress up the right side of the phone. Once you reach the top, stop. Then go back to the bottom and work across the bottom toward the opposite corner. Once you reach the bottom left corner, you'll work up the left side and dislodge the last bottom clip, before you hit the card slot door.
For me, the best way to get the left side open was to open the card door and work my fingernail under the back cover on the left side at the top of the card door. Once you get that side started again you'll continue up that side to the top. Now, before you try to take the back cover off, you need to know that the cover is affixed to the battery by double-sided tape on the battery.
(*EDIT*, there are also two small strips of double-sided tape along the bottom edge where the microphone is. These come free almost instantly but simply remember they are there so you don't get them covered in dust or dirt. They will stay affixed to the back cover, whereas the one on the battery will remain on the battery. Also VERY IMPORTANT!! The noise cancelling Mic is on the back where the cover is affixed. There is a very small somewhat oval or more teardrop shaped foam rubber stickie around the Mic, that creates a seal between the mother board and the back cover to seal the Mic to the outside and prevent any internal noise from making it to the Mic. BE VEEEEWY CAWEFUL as you run your fingernail or tool by that Mic hole on the bottom at the back. If your tool is inserted too far, you'll mash up the foam seal.)
You CAN get the cover free of the battery without destroying the double-sided tape, but you have to be patient and not push it. It takes about 10 minutes to get the cover free if you go slow enough and in order to keep the tape from ripping.
The trick to getting the tape free of the cover is to apply gentle prying pressure as you pry the cover loose, but don't try to peel it off. Instead, let the tape release itself gently. I found that steady and slow is the way to go. I just stuck my finger in there and let the cover work itself loose without applying any additional pressure. Once you finally free the tape from the battery, the top edge of the cover is the last part to free. That will come off easily by simply lifting the cover like a hinge, up toward the top of the phone, and the last row of clips at the top will release. Once off, be careful to protect the inside of the phone, and particularly the double-sided tape on the battery from dust and other debris.
After you release the cover, there is a Fluorescent Orange rubber cover over two Torx screws. Those screws keep the contacts for the battery firmly pressed onto the mating contacts on the motherboard. Simply lift the cover, remove the screws, and the connection simply lifts off with NO pressure. Then just grab the tab on the side of the battery and lift out. You're done. Now all you need to do is put the new battery in, hopefully it came with the double-sided tape. If not, get some from a craft or office supply store. Two standard width strips side by side should give you the proper coverage.
I also own an iPad 2, which I'm typing this on. I've had multiple iPhones on both AT&T and Verizon. I've also owned multiple Android devices on Verizon. I'm familiar with force closes. iPhone will close apps on you too. It just doesn't show a dialogue box. But I've had fewer force closes on my RAZR than any other Android device. As for battery, all of my phones batteries suck because I'm constantly playing with them 
hmy:, but I believe it's Apple flavored 
!