You open it. The PSP GO's internal battery is no more impossible to replace as a PS3 controller's is.
That being said, I strongly advise you to buy a PSP 2000 or 3000 instead of the GO. Bigger screen, more battery life, cheap micro SD to memory stick pro duo adapters, UMD support, homebrew options, easily replaceable batteries, better feeling controls, the list goes on and on. The GO isn't bad, but its a poor substitute for the glory that is the PSP 3000 running custom firmware.