To obtain RetroArch go the the official site it can be found at retroarch.com and download the version for your operating system or device. If you are using a Linux based operating system use the package manager (Software Center) for your distro. The majority of Linux distros include RetroArch in their repositories. It is also a good idea to go through the documentation to familiarize yourself with RetroArch and it's features, the documentation is located at Libretro Docs.
When you first install RetroArch and open it for the first time it will instruct you to go to the "Online Updater" in the Main Menu to update its Assets. In the "Online Updater" menu you will find the "Update Assets" option. With the "Update Assets" option selected press "Enter" to start the update. Once you do that you will see all the other menus, options and icons appear. When that is done be sure to also update GLSL Shaders, Slang Shaders and Joypad Profiles.
Next you will need to install "Cores", RetroArch refers to emulators as Cores. In the "Online Updater" menu enter the "Core Updater" menu and select the Cores you will need in order to play the ROMs you have. If you are new to emulation here is a small list of Cores I find to work pretty well.
*Commodore 64 (C64) - Vice
*Nintendo Entertainment System (NES) - Nestopia
*Super Nintendo Entertainment System (SNES) - snes9x (2010)
*Nintendo Gameboy / Gameboy Color / Gameboy Advance (GB/GBC/GBA) - mGBA
*Nintendo 64 (N64) - Mupen64/ParaLLel
*Sega Master System / Sega Genesis/Mega Drive / Sega CD / Game Gear (SMS/SG/CD/GG) - Genesis Plus GX
*Sega Saturn (SS) - Yabause
*Sega Dreamcast (DC) - reicast
*Nintendo GameCube (GC) - Dolphin
*Sony PlayStation (PSX) - Pcsx-Rearmed/Beetle PSX HW
*Sony PlayStation Portable (PSP) - ppsspp
If you would like to learn more about the various Cores/emulators for RetroArch I suggest taking a look at the Core Library: Emulation section in the Libretro Docs as well as the emulators section of the RetroPie Docs, I have found both to be very informative.
Due to the nature of emulation you may find some ROMs a bit tricky to get working. If a Core does not work with one of your ROMs try installing another Core from the "Core Updater" to see if the ROM will work with it instead. Make sure to are use an appropriate Core for the ROM you are having difficulty with. It also helps to do research in order to find out if there are any known issues with ROMs or Cores. *I did not include a Core for the PS2 because there isn't one for RetroArch, see the notes at the bottom of this post for a more detailed explanation.* When your done installing the cores you should also "Update Databases."
At this point I would recommend restarting your computer, I have noticed that in order to use a recently installed core or to add ROM files to the Playlist for the recently installed Core that a system restart is required for everything to work properly.
Adding ROMs to the RetroArch Playlist is done by going to the "Import Content" menu (the plus icon) and select either the "Scan Directory" or "Scan File" to add your ROMs to the Playlist. Please be aware you will not be able to add a ROM to the Playlist if there isn't a Core installed to emulate it's system. For example to add SNES ROMs make sure one of the snes9x cores is installed. Also keep in mind that if you scan a directory or file twice you may be adding multiple entries of the same ROM. So, if you scan a directory and notice that a ROM or two were not added to the Playlist don't scan the directory a second time instead use the "Scan file" option or use the Desktop Menu.
If you are unable to add some ROMs to the Playlist and do have the required core for the system installed you can always add ROMs manually with the Desktop Menu. Go the the "Main Menu" and select "Show Desktop Menu" this will open the Desktop Menu. To add a ROM select the console for the ROM you wish to add from the Playlist coloumn on the left side of the window. Then right click in the center pain of the window and select "Add File(s)". When the file manager opens navigate to where your ROM file is located, select it and add it to the Playlist.
Some commonly used hotkey commands for RetroArch:
F - Toggle between fullscreen and windowed mode
ESC - Close RetroArch
F1 - Menu toggle (pauses the game and brings up the RetroArch menu)
Volume Up - add button (plus sign)
Volume Down - subtract button (minus sign)
For more hot keys or to configure hotkeys and setup your Joypad go to the Settings menu (icon with 2 gears) and enter the "Input Menu."
*PS2 Emulation Notes*
If you do want to emulate PS2 games there are the PCSX2 and Play! emulators. PCSX2 is the more mature of the two at the time of this writing. PCSX2 requires a multi-core 3.5GHz capable CPU in order to emulate games at or near full speed as well as needing SSE2 and AVX2 support with said CPU. Also of note PCSX2 will more then likely never get a Core for RetroArch due to the way it was designed, this is not a slight against PCSX2 just what I was able to understand from RetroArch developers. Play! is still very young by comparison however, it is the more likely of the two to one day have a Core for RetroArch due to the way it's being designed. So, if you want PS2 support in RetroArch I would encourage you to help support the developers working on Play! if you can.