I took a USB flash drive to a friend and we copied a couple of games of his Xbox 360 to my drive, but when I took it home and put it in my Xbox it said that it couldn't launch it
When you download a game onto the Xbox consoles, you are required to be signed in to an account with purchase rights, in order to run the game. In this case, you can not play the game without being signed in to your friends Xbox account.
When you install a game onto the Xbox consoles, you are required to use the original disc, when playing. In this case, you would still need to borrow the discs from your friend.
The only way around this is by using the "home console" feature in conjunction with downloaded games. This is likely not ideal, as it effectivley requires your friend to sign in to your Xbox, and mark that console as his primary device.