
Okay, so if you don't want to use exploits like that guy in Riften and if you don't want to use console commands and if you don't want to spend a crapload of money on Trainers that you must seek out, but a fair way to grind up speech then here's my way of gettign Speech up.
READ:
If you have a better way to get Speech up without using exploits or console commands then feel free to state them so that I can update the OP with those methods as well.
If you already know how to get Speech up then don't come here and whine about the thread, cause some people don't know how to get Speech up. (I for example was flabbergasted at how I was suppose to get Speech up on my previous character that I put in 90 hours on.)
Gabriel77dan's Method:
Anyway, first up go to http://elderscrolls.wikia.com/wiki/Revyn_Sadri and have him train you somewhat good skill level, say 50 so you can get the perk Persuasion.
After this, go to any hold with many guards and pickpocket something and get caught, then use Persuasion to ask the guard to look the other way.
If you succeed; go talk to every guard in the city and do it over and over again to slowly raise Speech.
[WARNING] Do not talk to the same guard twice, cause you cannot persuade him or her two times, you could try Intimidation though.
[NOTE] I have not yet tested to see if a character 'right off the bat' with a really low skill can do this so that's why I suggest going to Revyn and training your skill a bit.
Old Method:
Pick up everything you can find (misc items) and sell them one at a time to merchants.
Feel free to add your own methods of how to get this skill up without using exploits or cheats.




