I have not noticed any mini-games like from Oblivion, which is good haha. But the only time I notice my speechcraft leveling is the rare occurance of meeting an NPC which you can bribe, intimidate, or persuade. Also, it seems to go up as I sell stuff....very very slowly. Is there a minigame or anything that enables you to actually train it? I've found topics concerning the exploit with the theives guild or something but prefer not to exploit the game, also, I dont want to get a very high character based solely on speechcraft haha.
Buying and selling things gets up as well as successfully persuading or intimidating. There's an exploit at the meadery in Rifton, talk to the guy behind the counter and ask him about the black briars, you're then given the option to persuade him and keep doing so. You need at least 26 speech to successfully persuade him though. --- http://www.planetdan.net/pics/misc/dammedance.jpg