It works much the same as any other console, afraid this will be generic rather than game specific at this point
1) You cut them out of screenshots
2) You dump them from VRAM, possibly with the aid of cheats. Usually with an emulator but you have some debug/memory reading in game options.
http://ppsspp.org/ is actually pretty good, especially if you are hacking rather than playing (its debug options are not bad for the state of the emulator development)
3) You rip them from the iso.
1) is horribly tedious and nobody wants to do it that way, however sometimes it is useful if the sprites are constructed from lots of things. If your emulator/cheats work well you might also be able to disable graphics layers to make this easier.
2) If you can dump the video memory you can either try emulator debugging options or run it through a tile viewer of its own. Cheats to do things would be things like cheats to make you have weapons, characters, enemies... you would not see until later in the game face you by being forced to.
3) Arguably the best way to do things. First you want something to peer into the PSP iso file, most would not look much further than UMDgen for poking around PSP games and I am inclined to agree.
PSP games are odd. Sometimes they stick close to the hardware and leave you needing something like
http://code.google.com/p/tiledggd/ , sometimes they come as a very common format (quite literally something like PNG or BMP, especially in visual novels and things that started out life as the same) and other times they are some intermediary format like we deal with at most other times in ROM hacking.
Nothing stopping you from combining a few methods -- if you find the files for say the end boss but can not decode them then you can sometimes overwrite the basic enemies and then have the end boss display when the game thinks it is just displaying the normal enemy before dumping the lot with a normal emulator VRAM dump.
I should also note that this is a 3d game so you might not be seeing normal sprites, model ripping is certainly doable but it tends not to net things as nice as sprite sheets.