Generally you need to find a site with an emulator, often something along the lines of 'www.gbaroms.com' or whatever (ROM is the name given toi the game file), and download it (different ones are available for different consoles that you want to emulate). Then you download the individual game ROMS (files) from different sites that will basically let you play the game on the emulator for that game's console. To open the game file, you'll need to open the emulator itself, go to 'File' at the menu bar, then select 'Open' and find the game ROM that you've downloaded. Saving will usually be done in-game as usual.
This is a generalised account based on emulators I've downloaded and used, though. Other ones may be different.
[small]NOTE TO MODS AND ANYONE ELSE INTERESTED: I do not in any way endorse game piracy and stealing. To anybody helped by my post, please don't go ahead and download games that are still copyright or that you don't own. If you own a game then download it by all means, and if it's freeware or abandonware then also go nuts. But don't use my advice to pirate games. Piracy is wrong, and hurts game developers and publishers financially. Thank you.[/small]