See this XDA thread for the original discussion: http://forum.xda-developers.com/showthread.php?t=1528782
The Nexus extended battery is available online and at Verizon stores for $25. I purchased from Verizon in order to be certain I was receiving an OEM battery.
Step 1: Tools Required
This picture shows how much material I removed during the modification.
Step 2: Trim the Back Side of the Battery
Don't use the battery as a cutting board. Instead, peel back the battery a bit and slice it without touching the battery body.
Step 3: Trim the Front Side of the Battery
Some have removed the sticker altogether, but I wanted to take off the minimum amount of material possible. The left side of the battery (from the perspective of the photos below) is where the sticker overlaps. Along that left side, which is closest to the cover snaps, the overlap adds to the overall thickness of the sticker. Most phones' covers will not snap closed along this side of the phone. I have pointed to the edge of the overlapping area with the knife in a picture below, but this was taken after I trimmed it.
In order to reduce thickness while leaving the battery looking as intact as possible I first peeled back the sticker revealing the NFC chip. With the visible part of the sticker peeled back, I was able to then access the edge of the sticker it covered. Peel this edge back and cut it with your knife so that the sticker edges no longer overlap. I was not very neat with my cut. If you scribe a light line using your knife along the edge you will cut using the top edge as a guide you will be able to follow that line and make a straight clean cut.
Do not use the battery as a cutting board when you trim the sticker. Peel the sticker back and slice it.
Step 4: Finished Result
Enjoy your extra battery life, heavier feel, and tighter battery compartment.