1) Find your Super Meat Boy folder (should be
in Program Files > Steam > Steamapps > Common.
2) Open your Super Meat Boy folder and create a folder named "Levels" no quotes.
3) Place the level file from the .zip/.rar into the folder you've just created.
4) Start the game in -devmode (from the command line in "set launch options" if you right click the game from Steam, just enter that line in).
5) When the game loads, press F1 to enter the editor and click load in the bottom left corner.
6) Finally, type the name of the level you want to play exactly as it appears in the file name. Press F1 again to leave the level editor and play the level.
To get back to the game as it normally is, just delete the entry in the command line.
*Images from http://supermeatboy.com/69/Devmode_leaked_/
**Thanks to RockLeeSmile for the steps**