So I downloaded Krita for a couple reasons:
1) It was free
2) GIMP doesn't like my tablet at all
3) Has plenty of functions

I was using this for the first time today and everything was going all hunky-dory. I was drawing. The tablet was working. The program was running. Everything was good, until the input started to slow down. My strokes weren't being input on time and sometimes not at all. I closed the program to see if there was something else running in the background. I opened task manager and looked at running processes to see what was taking up the most memory and it just so happened to be Krita using 1218916 KB of memory. That's a little more than 1GB of memory!!!!! And the program was closed as well!

My question is: How in the heck do I make it not take up that much memory? Is there someway that I can limit the amount it uses?

I want to be able to use this program. I don't want to have to go back to GIMP... please help me!

You could try working with smaller (lower resolution) images.
If you work with high color depth (16bit) you could switch back to 8 bit color.
Other than that i am not sure what can be done: 1 GB is really not much for graphics work.
Maybe someone else knows some option to reduce for example the undo buffer size or something similar.
I am sorry that i can't help you better.

Why shouldn't it use so much memory?

Remember, RAM is only being reserved for a programme until it is requested elsewhere. Don't think that it is taken as such. Allocation is the job of the kernel and if resources are not needed elsewhere so be it.

Nothing to worry about.

Currently, Krita's ram usage is pretty simple to calculate: width * height * number of channels * channel size * number of layers. Well, there are complications. If you use filter layers or masks, that will add more memory usage, and there's undo information. On the other hand, a transparent layer with only a few dots won't allocate memory for the full width * height. By default Krita will try to use up to half your available memory, after that, we'll save memory out to temporary files.

If Krita is still running after you've closed the last window, that's something to look into, though.