Since you're not registered I can't tell whether you're in warm or cold water area... so get a full length suit.... a mask and snorkel.... fins... and if you can a weight belt, many dive stores won't sell you weights without proof of dive certification. Just be aware that the wetsuit makes you more bouyant so you will find it difficult to stay underwater. A real useful tool is a plastic handle with suction cups...this will allow you to hold yourself steady while applying pressure with your cleaning tools. I have strung a length of rope under the hull, athwartship, to pull myself down when I didn't have the handle and weights, but it was much more difficult.
Use a soft bristle brush with an extension handle, or one of those short handled winshield cleaning tools with the sponge on one side and a squeegee on the other, or a handheld rag or sponge for basic slime. Don't use anything stiffer than you absolutely need, because you'll just be scrubbing off paint too. You may need a scraper for the "crusties" but be judicious with it.
A 36 foot boat will have a fairly deep draft, making it difficult for an inexperienced diver to get down to the bottom of the keel. This is why you need the weights or rope.
My buddy in Florida has always cleaned his Island Packet 31's bottom himself. He has a tank and mask, weight belt, etc. always takes it when cruising so he can dive on the anchor.... Most times, however, he just warps his boat in close to shore in shallow water and simply walks along the bottom with his soft bristled brush. His boat has a center board, so it's draft is like 2 or 3 feet with the board up, making it very easy to get the boat close in.
That said, a 36 footer is going to be significantly more work than my 27 footer, I don't envy you, but I think it's important that everyone experience cleaning their boat's bottom at least once.
