I mentioned trainers in the previous post when I talked about training mage skills. You can find trainers for any skill in the game. The UESP site has a page listing the trainers. You can only train five skill levels each time you level up. Whether it's leveling five different skills once or one skill five times, you only get five slots. And Trainers cost gold. The higher your skill, the more it costs per training session. The site does list ways around the cost, but hey, I'm an honest person so I'll pay good gold whenever I want to fast-train a few levels.
Really, I don't use trainers for every skill. My favorite skill to fast train is Armorer because I want to get it up to Journeyman (lvl 50) as quickly as possible so I can fix my own enchanted armor and weapons. Until then, if I have an enchanted weapon or piece of armor I'm using, I have to pay a bit of gold to a Smith to fix it. And if you don't fix your armor and weapons, they will eventually break and be totally useless to you. After Journeyman, I just fix my own armor/weapons after a dungeon crawl. If I've been training up my armor and weapon skills in the dungeon then I'll fix them after each altercation.
It's always a good idea to fix weapons and armor that you plan to sell, because until your Mercantile skill reaches Apprentice, the price you get for any goods not fixed to 100% is reduced. Once you reach Apprentice, the condition of armor/weapons is not taken into consideration (but I would still fix things before selling them, just to continue training your Armorer skill.). A Journeyman skill will allow you to sell anything to anyone. This means that you can sell clothing to armorers, where before all you could sell them was armor/weapons/soul gems/gems/animal pelts. General merchandise stores will already buy anything from you and alchemists will only buy apparatus/potions/ingredients/books/scrolls/pelts/gems Once your skill reaches Expert, you can invest in a store, and once your skill reaches Master you can buy/sell at a 100/100 ratio, plus the store will have 500 more gold (in addition to any gold you invested) to trade with. This is another skill that would be worth paying a trainer for to fast-track.
Once any skill you have reaches Expert, the only way you can get a Master Trainer is to ask about one. When you find a Journeyman Trainer in the field you want to train up, the Training dialogue will pop up and if you ask about it, they'll tell you where the Master Trainer is. To get the Master to train you, you will first have to pass a quest that they give you. Once that is done, you may use them to continue training you, at a price, of course.
So, that's how you can fast-train your skills.