See listen kid...firstly this explanation is long, but it has every thing you need to know in detail...ok now we'll start the explanation.....there are many game boy emulators which you can download
the best one for a game boy rom (the game files are called roms) is 'visualboy advance' known popularly as 'vba' for short(I think the latest version is 1.7.2 but any version will do). To play a rom(gameboy game file) double click the icon and a window might appear saying if you want to run the file, cilck run, then another window will appear, click file from the menu, then click open/open gameboy(same thing), then search for the rom file(gameboy games file) and double click.
I downloaded my vba from this site http://www.gameboy-advance-roms.com/gba_emulator.htm
just scroll down a bit and you'll find 2 purple gamboy advance type icon thingys....click the first link then on the next page click the link you see then just follow the rest and download according to your computer system(for windows chose any of the first three links)
This emulator can play gameboy black and white games(file extension is .gb) , gameboy colour games(file extension is .gbc), and gameboy advance games(file extension is .gba) only!! not gameboy NDS, gameboy NES, or gameboy 64, for these gameboy games you need other emulators go to this site for emulators http://www.emulator-zone.com
BUT games also have to be downloaded and this site does not offer copyright roms(gameboy games files)
but dont lose hope...there are other sites from which you can freely download roms(gameboy games files) you can download the games then try and see if they work on your emulator. If they work properly, then I WOULD SUGGEST YOU TO PLEASE BUY THE ORIGINAL GAME CARTRIDGE because it is actually ILLEGAL TO JUST DOWNLOAD THE GAME FOR FREE (I suppose you've heard of the word piracy or pirated cds??)to search for a game just type the game name followed by roms for example, you want the pokemon emrald game right?? so just type "pokemon emerald roms" in the search bar of a search engine(such as google) you may get a huge list but be patient and search through the sites and you'll find it. heres a site from me to you (^_^) http://www.mxemu.com/romshare.php
If you cant find any rom that you want then search another site.
And make sure that your anti-virus program is good or your computer could get infected and break down(and that is not what you want to happen...trust me)
BUT AS I SAID EARLIER I WOULD SUGGEST YOU TO PLEASE BUY THE ORIGINAL GAME CARTRIDGE
Other than that....happy gaming!! Hope this solved your question(^_^)