The Trainers of Skyrim

There are many many different trainers in Skyrim. All of which have a specific level; Journeyman, Expert, and Master trainers.

TIP: Don't go right to Master trainer for anything. Start at Journeyman and work your way up, unless you like becoming overpowered.

"Combat Skills: The Path of Might" trainers
Smithing:

Journeyman Trainer; Ghorza of Markarth.

Expert Trainer; Balimund of Rifften.

Master Trainer; Eorlund Grey-Mane of Whiterun.

Heavy Armor:

Journeyman Trainer; Hermir Strongheart of Windhelm.

Expert Trainer; Gharol of Dushnikh Yal (The Reach).

Master Trainer; Farkas of The Companions (Jorvaskar, Whiterun).

Block:

No Journeyman Trainer for this skill, so skip ahead.

Expert Trainer; Njade Stonearm of The Companions.

Master Trainer; Larak of Mar Khazgur (The Reach).

Two-Handed:

No Journeyman Trainer for this skill, skip ahead.

Expert Trainer; Torbjorn Shatter-Sheild of Windhelm.

Master Trainer; Vilkas of The Companions.

One-Handed:

Journeyman Trainer; Armen of Whiterun.

Expert Trainer; Athis of The Companions.

Master Trainer; Burguk of Dushnikh Yal (The Reach).

Archery:

Journeyman Trainer; Faendal of Riverwood.

Expert Trainer; Aela the Huntress of The Companions.

Master Trainer; Niruin of The Thieves Guild (Riften Ratway).

"Stealth Skills: Path of Shadow" trainers
Light Armor:

Journeyman Trainer; Scouts-Many-Marshes of Windhelm.

Expert Trainer; Grelka of Riften.

Master Trainer; Nazir of The Dark Brotherhood.

Sneak:

Journeyman Trainer; Khayla, of the Khajiit Caravans.

Expert Trainer; Garvey of Markarth.

Master Trainer; Delven Mallory of The Thieves Guild.

Lockpicking:

No Journeyman Trainer for this skill, skip ahead.

Expert Trainer; Majhad of the Khajiit Caravans.

Master Trainer; Vex of The Thieves Guild.

Pickpocket:

Journeyman Trainer; Ahkari of the Khajiit Caravans.

Expert Trainer; Silda the Unseen of Windhelm.

Maser Trainer; Vipir of The Thieves Guild.

Speech:

Journeyman Trainer #1; Dro'marash of the Khajiit Caravans.

Journeyman Trainer #2; Revyn Sadri of Windhelm.

Expert Trainer; Ogmund the Skald of Markarth.

Master Trainer; Geraud Germaine of the Bards College (Solitude).

Alchemy:

Journeyman Trainer; Lami of Morthal.

Expert Trainer; Arcadia of Whiterun.

Master Trainer; Babette of The Dark Brotherhood.

"Magic Skills: Path of Sorcery" trainers
Illusion:

No Journeyman Trainer for this skill, skip ahead.

Expert Trainer; Atub of Largashbur (The Rift).

Master Trainer; Drevis Neloren of the College of Winterhold (Winterhold).

Conjuration:

Journeyman Trainer; Runil of Falkreath.

Expert Trainer; Phinis Gestor of the College of Winterhold.

Master Trainer; Falion of Morthal (Radiant quest: Curing Vampirism).

Destruction:

Journeyman Trainer; Wuunferth the Unliving of Windhelm (Side Quest and obtainment of house: Blood on the Ice).

Expert Trainer; Sybille Stentor of Solitude.

Master Trainer; Faralda of the College of Winterhold.

Restoration:

Journeyman Trainer; Keeper Carcette of the Hall of the Vigilant (No access after first Dawnguard DLC Quest: Awakening, seeing how the hall is burnt down and everyone dead).

Expert Trainer; Collete Marence of the College of Winterhold.

Master Trainer; Danica Pure-Springs of Whiterun.

Alteration:

Journeyman Trainer; Melaran of Solitude.

Expert Trainer; Dravynea of Kynesgrove (Eastmarch).

Master Trainer; Tolfdie of the College of Winterhold.

Enchanting:

No Journeyman Trainer for this skill, move ahead.

Expert Trainer; Sergius Turrianus of the College of Winterhold.

Master Trainer; Hamal of Markarth.

Improving Skills: Skill Books
Scattered throughout Skyrim are a number of rare Skill Books, each associated with a particular skill. The first time you read each book, the associated skill increases by one.

There are five different named books for each skill (90 different book titles), so a diligent collector can potentially increase each skill by five points.

It's worth noting that there are multiple copies of each book in the world (usually 3-5). However, you only gain a skill point the first time you read a book - rereading that book, or any of it's copies, has no further effect.

Improving Skills: Augmentations
There are a variety of different ways to temporarily boost your skills (or their primary effects):
 * Equip enchanted items that increases that skill
 * Drink a potion that boosts that skill
 * Aquire a Shrine Blessing or other temporary bouns to the skill

General Advice on Improving Skills
When improving your skills, heed the following advice:

In general, it's better to increase your skills and level up naturally, rather than trying to find ways to exploit the game. In fact, it may make your adventure harder, since you'll lack the gear and tactics needed to survive higher-level combat.

There is no fixed "maximum level" (i.e. Level 50) for you to attain. However, if you were to raise all of your skills to 100, this would - eventually - take you to around level 80. As you're only able to choose one perk each time you level up, and there are well over 200 skill-based perks, don't fixate on obtaining all of them, as it is impossible. Instead, focus on improving skills you're most interested in, and ignore perks you won't take advantage of, even if they're in a skill you use constantly.

Statistically, it's better to save Skill Books for higher levels, when the amount of effort or the cost of training needed to increase a skill rises dramatically. However, this tends to be difficult to do in practise, since you automatically read a book when picking it up, and won't know in advance that it's a skill book. Unless your intent is to raise every skill to 100, it's best not to worry about this.

If you're most of the way to your next level and just need one or two more skill increases, here are some options:
 * Do you have any skill books you haven't read? Read them!
 * Are there any ingredients you haven't sampled? Especially at low skill levels, your Alchemy skill rises quickly just by eating common ingredients and learning their first effect
 * Do you have a lot of ingredients? You may be able to make potions. Try your hand at Alchemy!
 * Do you have any ingots or smithing supplies? You might be able to forge or improve something. Attempt smithing!