Ok so I just took 45 minutes to find and kill the enderdragon! BUT! I have the new Xbox 360 disk for minecraft and I hit the egg... AND IT BROKE DX What do I do to collect it?
Here's a pretty good video for obtaining the ender dragon egg on the XBOX360 version:
Note: I did not make this video and do not take credit for it.
Source: I've used this video to collect the ender dragon egg on console version.