When starting the game, unlock the cars then just run everyone over. The rocket launcher car is recommended; if need be you can use the rockets to kill the flying things.
First, complete the game and make sure you are about level 40 with your first character. Start a split screen game with a new character that you want to level up fast. Find an area with plenty of enemies that are easy to kill (for example, the lost cave with the crabs and leveled up Skags). Make sure your high level character was saved in the area you wish to go to, and load them as the host with the other character as the second player. Leave them by the new-u station and go to town with your high level character. Your other character will gain levels almost instantly. This starts to slow down about the mid to high level 20s, but you will be able to level them up to about level 35 relatively fast When start a single player game with the lower character, you will start out with an extremely high level character and be able to play through the game easily and collect more loot. This is an excellent way to make many different characters.
Note: A high level friend is required. Have your friend join your game and travel to high level places. As you stand back, watch your experience fly in the 8000s as your friend takes out enemies due to experience sharing. This is also a good way to get high level items.