You can use the same screwdriver to undo the cover as you used for flashme. Usually the spare batteries should come with a screwdriver to open it. I've only had experience with GBA batteries. I got the logitech one and that lasts 30% longer than the original GBA one.
i just bought one from dealextreme it came with a screw driver, it lasts about 3 hours while my old one lasted 4, (i had to replace my original, it was only lasting 1 hour fully charged, i left it out on the porch one day when i was using the outside charger, bad idea especially since im in california and this heat wave killed it).
I emailed Nintendo a while back asking if they were planning to release any longer life batteries (kind of like how Sony has the 2200maH gold one), but they said they have no current plans, and do not recommend you use 3rd party batteries (then again they don't recommend you do anything else except buy their games).