Need Advice on Cleaning up After Water Heater Leaked.

First -- the immediate things! Don't clean the carpet at this point, focus on DRYING it as quickly as possible, and the pad underneath too. Have you yanked up the carpet AND the padding that is under it, exposing the floor underneath ? If not, do so right away (and keep the kids out -- those wooden strips that hold carpet near the walls are full of nasty points-up nails).

Even getting up the water with a carpet cleaner likely won't get the padding, which is foam, dry enough to avoid molding; you need that carpet and padding pulled up, but not necessarily replaced -- get it all dry enough and you may well be able to put it right back down yourselves. Pull it up only to the point where the wetness ends; you don't necessarily have to yank it up throughout the room. Then you need to rig ways to prop up the carpet and padding, and then rent an industrial-type fan (house fans won't do) from a Home Depot type of store and blast it at the wet carpet and pad and wall.

While one of you starts this, the other should call in a company that specializes in water cleanup. The water very likely soaked up the wall like a wick on the inside where you can't see it. A good company should be able to test whether that happened and should work with you on mold prevention measures, which may involve spraying the wall with a mold inhibitor chemical.

Go to the library and look in whatever is the Chicago version of "Checkbook" (I believe they're in other cities -- in the DC area we have "Washington Checkbook and it's like a local version of Consumer Reports with listings for local businesses; it does not accept advertising and does not let businesses pay to get listed, but it does do reviews of local companies. You need a reputable one!).

Yes, we've had water leaks too, and pulling up wet carpet and the padding is vital to getting it dry and avoiding mold.

My brother had just bought their house when a pipe broke and flooded half the basement. The Mold would come from the foam under the carpet so he kept the carpet just removed the foam and let the floor dry then put the carpet back down.

rent an industrial strength dehumidifier and let it run down there for at least a week. Make sure you have a drain or sink for the hose so you don;t have to keep emptying a reservoir. I think you can get them at Home Depot

Hire someone.
there is probable likelihood, that the water damage... is elsewhere.
In the walls where you cannot see it.
And who knows where else, the water has puddled or accumulated etc.

My friend, who's plumbing leaked, the bathroom, they had to tear down a wall because, the broken pipe was in the walls and water in the walls too.