Well, other than the obvious training, I have found that the easiest thing is to just sell things to vendors. You get moneys, while getting speech experience. You can also bribe/initimidate/persuade...etc...
NOTE: The amount of skill progress gained is based on the base value of the item being bought/sold. However, if you trade multiple units of an item in one transaction, you will only gain experience equivalent to trading a single unit; for optimal leveling, sell each item one at a time, and sell expensive items.
From UESP