How can I repair a toilet that is leaking at the base?
This is a tough job and it may be worth it for you to call a plumber as there are numerous complications you might encounter. However, you will have to learn somehow:

1) Forget about the "higher pitch dripping sound" for now. The leak at the toilet base is big trouble and your efforts should be focused there.

2) shut off the water supply, flush the toilet, use a plunger to force remaining water out of the bowl and down the drain, use sponges and towels to sop up all remaining water in the bowl and tank.

3) Pull the toilet: your toilet is held down to the floor with two special bolts (closet bolts) that are either hooked under a ring set in the floor (closet ring) or screwed into the floor itself (less common). You need to remove the nuts by unscrewing them or cutting them off. Pulling the toilet off is a two person job (I have done it alone but I hurt my back doing it). Make sure you have an open area with a tarp or something to set it down on.

4) there is a donut shaped ring, usually made of wax but sometimes foam or sometimes wax with a foam core, which seals between the toilet and the closet ring. Scrape all remnants of the old wax seal off the bottom of the toilet and the closet ring. Inspect the closet ring so you see how the new bolts hook under the slots in the ring or screw to the floor. If the ring is broken, if the floor is damaged badly, if the piping is compromised: stop and repair any of that stuff prior to reinstalling the toilet.



5) reinstall: attach new closet bolts to the ring (or floor if that is the case) using threaded clips or nuts to secure the bolts to the ring. Place new wax ring in the sun for a bit to let it soften some (or warm it up with a hair dryer), than press it onto the bottom of the toilet at the waste outlet OR place it on top of the closet ring. Carefully lift the toilet and lower it down over the bolts (2 man job perhaps). let it gently squish down onto the wax, crawl up on the toilet some to bed it firmly. Hand tighten the nuts on the closet bolts, moving back and forth from one to the other, ensuring even tightening on both sides. Snug them up with a wrench, do not over tighten or you may be buying a new toilet. 

There are a lot of issues and complications you could encounter. Buy a couple wax rings when you are at the hardware store in case you wreck one.