Note: 100% or more Invisibility or Chameleon is required. This is done by either enchanting a number of armor, rings, or amulets, or entering an Oblivion Gate and repeatedly reloading the game until you find the Sigil Stone that offers Silence and Chameleon. After you get that stone, use the "Duplicate item" glitch and you can now instantly enchant your items without the trouble of finding Soul Gems and Souls. Now that you have Invisibility, go up to a guard and start beating him up using hand-to-hand combat. When he dies, more guards will keep spawning. You can just keep beating on them. You can also find a character that is marked with a crown that will not die, and only becomes unconscious. Since they do not see you, it is not bad. Also, they never die, so you can endlessly hit them until you master Hand-To-Hand. Your skill increases about every 20 seconds or more, depending on how high your skill level already is.
Go to the Arena district in the Imperial City to find two NPCs (an Argonian and an Imperial woman) fighting. Stand close to them for a minute. Your Hand-To-Hand skill will increase by 5. Note: This can only be done once.
While in the Fighting Guild, you can watch to people training and your blade and block will increase.