You need a jailbroken iOS device, running iOS 6. See the Downloads page for more info.
To emulate advanced systems like the PSP fast, the emulator needs to translate the machine code language of the PSP to the machine code language of your PC or mobile device at runtime. This is done with a "Just-In-Time recompiler" or JIT, also known as a Dynarec. PPSSPP has JITs for x86 and ARM.
For a JIT to function, an app needs to have the ability to generate machine code at runtime. This is allowed on Windows, Mac, Linux and Android, while it is completely disallowed on non-jailbroken iOS and on App Store Mac apps, and on Windows Phone 8.
You're probably a Windows user. Because x86 CPUs are damn fast, PC GPU drivers are good, we have a fairly advanced x86 JIT, it's written in C++ and I rock.
You probably run PPSSPP on a mobile device. The ARM JIT is basic and needs improvement, and these devices simply are not very strong yet, no matter what marketing tells you, or their graphics drivers SUCK. An example of the latter would be the Nexus S.
That's not a question. Anyway, you may need to install the VC2010 redist (some DLL files). Also, if it still doesn't work, try installing the latest DirectX and OpenGL drivers for your graphics card.
To legally turn your PSP games into .ISO files, you need to install "custom firmware" on your PSP and run some program to dump UMD discs or digital downloads into files. Tutorials for this can be found around the web. There are also tools to turn ISO files into CSO (compressed ISO) files to save space.
PPSSPP has built-in XInput support on Windows so it will "just work" with any Xbox 360 pad that you plug into your PC. On Android the gamepad situation is not very good yet, the Xperia Play buttons will work but not the touch sticks, for example.
Any reasonably modern CPU will be just fine, and any GPU that can handle OpenGL 2.1 should have no issues. You should make sure to install the latest graphics drivers available though. Windows XP or later is required, Windows 7 or 8 is recommended.
Buy PPSSPP Gold for Android! It's the same as the regular version functionally, but by buying it you support the development of PPSSPP.
Alternatively, feel free to toss a bitcoin or two to 13KFhiBiFDjQAfXrBn3z5VgNKULP6DzdHb :)
CSO are compressed ISO files that can be played directly, decompressing on the fly. Very useful to save space on your Android device, for example. There are a large number of programs around the web that can create CSO files from ISOs, just Google for it.
You can either help out with fixing it, or wait until someone does.
Nobody has volunteered to prepare and package one yet. Contact me if you're interested.