First, you will need a lot of money, depending on the skill you wish to train. Next, you will need to find someone who teaches that skill. Once you have done both of those things, start training repeatedly in a certain skill, or multiple skills. As you probably know, when someone trains you in any skill, your level meter goes up 1/10. Train ten times, or however many times it takes you to level, to level up. To control the multipliers (relatively) you will need to know the governing attribute of the skill(s) you have trained in. When you train in something, the multiplier on the governing attribute of that skill goes up by 1x, to a maximum of 5x. You can have any number of multipliers, as long as they add up to ten. Note that certain skills take more to train than others, and as your skill increases, so does the price of the training. The following is a list of trainers and their locations that can train their particular mastery up to 100 points. Note: Some of the trainers will require you to do certain things, such as get to a certain rank in their guild. Others will train you for your gold.
 
Skill
Name Location
Sub-location
Acrobatics Senyndie Fighter's Quarters
Waistworks - Vivec Arena
Alchemy Abelle Chriditte
Popylon Chamber Stronghold - Valenvaryon

Alteration Seryne Relas
Home Tel Branora
Armorer Sirollus Saccus
Lowest Level Hawkmoth Garrison - Ebonheart

Athletics Adibael Hainnabibi
Abidael's Yurt Kaushtababi Camp south of Molag Mar

Axe Alfhedil Elf-Hewer
Upper-Level Stronghold Falensarano

Block Shardie Courtyard
Buckmoth Fort outside Ald'ruhn
Blunt Weapon Faralenu Henim
Abbey of St. Delyn the Wise St. Deyln Plaza - Vivec

Conjuration Methal Seran
Lowest-Level Ald'ruhn Temple
Destruction Leles Birian
East of Piernette's Farmhouse Located east of Pelagiad

Enchant Quorwynn Near Exit
Stronghold Indoranyon
Hand-To-Hand Taren Omothan
SW Bedroom Lowest Level - Holamayan Monastery

Heavy Armor Seanwen Arena
Fighter's Training - Vivec
Illusion Erer Darothril
Dirty Muriel's Cornerclub Sadrith Mora

Light Armor Aerin Andus TRadehouse
Mar Gaan
Long Blade Ulms Drathan
Armigers Stronghold Molag Maar

Marksman Missun Akin
Missun Akin's Hut atop Stronghold Falasmaryon

Mercantile Ababael Timsar-Dadisun
Ababael Timsar-Dadisun' Yurt Zainib Ashlander Camp

Mysticism Ardarume West Wing
Gateway Inn - Sadrith Mora
Restoration Yakin Bael
Vos Chapel
Security Hecerinde Hcerinde's House
Balmora
Short Blade Todwendy
Lucky Lockup Cornerblub Balmora

Sneak Wadarkhu Dreugh-jigger's Rest
Gnaar Mok
Spear Mertis Falandas
Lower-Level Tower Dusk - Ghostgate

Speechcraft Skink-In-Trees-Shade
Mages Guild Wolverine Hall - Sadrith Mora

Unarmored Khargol gro-Boguk
Vacant Tower Dragon Fel