Don't get on my case about how this is cheating, but when I want to get my skills up fast, and theres a trainer in a faction I'm a part of, i do this.
Train however many times i can (depending on how much gold my char has)
FUS ROH DAG!
pickpocket at the moment when they are gettting up and take gold back
0 bounty, Skill leveled, no hostility.

I've tried this in multiple places with different factions/trainers. Dont know if it works with people who are not friendly, just neutral: random trainers.

Trick also works with paralyze potion.

If a follower will also train you (like Faendal), you can have him train you and then have him simply give you the money back

It does not bother me as you do not have anything to spend your money on anyway, so no I will not use this.

My main problem in the game right now is having way too much gold, so I would gladly pay a trainer tenth the price to train just to use my coin on something.

Same here. Early on I used the Faendal trick to save money to buy the Proudspire Manor house. But after I bought all the houses and upgrades, I find myself running out of stuff to buy. I'm literally buying and reselling stuff just to level up my speech skill, not because I actually need to earn money.