Emulation: PC side there are one or two emulators but they are at the same sort of level that the DS was at when ensata was leaked.
PSP side: The usual method is to install a custom firmware (there are chips which amount to the same thing but few people use them). Naturally Sony have not allowed this so people look for exploits, the current one that I believe works on all PSPs is the so called pandora's battery which works on all and on all firmwares (the older ones require certain games or were patched in a firmware update).
There are two options, the theory goes that when the EEPROM in the battery has certain data on it it goes into service mode.
There are two methods:
hardware: either buy one (Datel have a few and there are people selling premade) or build one: you crack open the battery and desolder a pin rendering the EEPROM unavailable and by extension creating a battery.
software: you can overwrite the EEPROM if you can run custom code (some of the newer slimline ones can not do this if I recall correctly) which means you need a friend with a homebrew capable PSP.
Now you have a pandora's battery you normally to downgrade the firmware to a lower one which can run custom code with before going to a custom firmware which has all the features of the official with a few nice tweaks like running isos.
All code be it homebrew, isos, PS1 isos is run from memory card save the two or three apps that can do some streaming over wireless so prepare to open wallet/sell first born etc to fund a decent sized card (it is not as bad as it was but it is certainly not nice compared to other stuff), Sandisk are usually a good route here. There are some hard drive mods and adapters but I will leave those to you to decide upon (by the time all is said and done in my opinion you might as well just have got a big card as it will cost you as much).
VVoltz has a thread to get you started:
http://gbatemp.net/index.php?showtopic=69140