At Riften, talk to a Dark Elf named Ungrien. Choose the ""Tell me about Maven Black-Briar." option and then the persuade option. After that, the persuade option doesn't disappear, allowing for infinite experience and maxing out your speech.
nillort eb i Currently playing: Pokemon FireBlue, Call of Duty: Modern Op 2, Tetris, Gran Turismo Auto 5: Liberty City
I up my Speech skill along with Smithing and Enchanting at the same time. After i have collected a decent amount of materials i smith and enchant all that i can and then just sell it all, it all eventually goes up. Or just use the exploit at Riften :/