The Simpsons arcade game is just weird, and not really related to the show very well. Of all things, you have to rescue Maggie from Mr. Smithers, who had just robbed a jewelry store.
But, that's what we have to work with, so we'll deal with it.
You play the game as your Simpson of choice and anyone else around the machine does the same.
You run along, beating the armies of identical twins, until you get to the end of the stage, then you fight the boss character, and then go on to the next stage. No surprises there.
However, the stages get pretty tough after a while, mostly because the amount of enemies you have to deal with at once gets pretty ridiculous.
But you have a secret weapon in your arsenal.
If you have a friend, or some random guy decided to play this game with you, you can make your characters do super-powered double-team moves. The trick is that you have to get them standing next to (almost on top of) each other to pull them off.
Once you get them standing close, just let go of the joysticks and all the buttons for a couple of seconds. Then someone will say a catchphrase and begin the attack.
It doesn't last too long, probably because it's a bit more useful than your regular punches, kicks, and vacuum cleaner shots, but you can do it any time you want... assuming you can get to a safe spot for a couple of seconds.
And this works with any combination of two characters you happen to have, so go nuts.