rise,

I think you have 2 problems: 1) the water is leaving the toilet tank and
2) the toilet valve is not replacing the water as it leaves the tank. Let's
look at the first problem. Flush the toilet and let it go through it's cycle
and refill. Add vegetable dye (left over from coloring the Easter eggs) to
the water in the tank. Go away for a few hours. Look in the toilet. Is the
water in the toilet now colored? If so your flapper valve needs to be
replaced. This is the black rubber thing at the bottom of the tank. If the
water in the toilet is not colored then look for a pool of colored water on
the floor around the toilet. If you find a pool look for a cracked
tank(unlikely) or a bad seal where the toilet and the tank bolt
together(likely).
On to problem #2. Remove the lid from the tank. Is the float arm hanging
in mid air? If so there is dirt or grit binding things up. Clean or replace
the float arm. Of the float arm is down then there is dirt or grit in the
valve itself. Clean or replace it.
Your local library has DIY books which will cover all of these repairs.
They are easy to do. Porcelain fixtures will chip or crack So, don't over
tighten things , don't drop wrenches on the fixtures, et c.

Good luck,
Dave M.