Ive added too many fish How can I keep them and my water healthy

I've recently bought a 10 gallon tank. I set it up without problem, I let it stabilize, and after that, I added fish. But what I didn't realize is you need to add only a couple hardy fish first, and then add more later. I put twelve small fish in right off the bat. After realizing the ammonia dangers, I went out to get an ammonia 4-6 week meter, and a product to remove ammonia. But now I notice the water is becoming alarmingly murky. The wall on the opposite end of the aquarium is getting closer to invisible. The ammonia meter reads in between "safe" and "caution." And I know I'm not overfeeding.

So basically the question is: How can I keep the twelve fish from dying, and how can I keep my water healthy and clear?

You're going to be walking a "tight rope" unfortunately for at least a few weeks. Without having too much information on the type of fish you have and what kind of setup you have in your tank, it's hard to give a clear answer.

From a guideline standpoint, you're right 12 fish for a 10 gallon tank is quite a load for a tank. Is it possible to cycle a tank that is borderline overstocked, yes, but it's going to be a lot of work.

To keep the water healthy and clear you're going to have to find the fine line between tank cycling and keeping your fish alive. You're going to have to do enough water changes to keep the ammonia and nitrate levels at an acceptable level for the fish. On the other hand, too many changes affect the tanks ability too cycle and may extend the cycling period significantly. Longer cycling means more time your fish are under stress.