so far I've spent all my money on training

Combat Skill Trainers

Heavy Armor
Journeyman Trainer
Find Hermir Strongheart in the Windhelm.

Expert Trainer
Find Gharol of Dushnikh Yal in The Reach.

Master Trainer
Find Farkas of The Companions in Whiterun.

Block Skill Trainers
Expert Trainer
Find Njade Stonearm of The Companions in Whiterun.

Master Trainer
Find Larak of Mor Khazgur in The Reach.

Two-Handed Trainers
Expert Trainer
Find Torbjorn Shatter-Shield in Windhelm.

Master Trainer
Find Vilkas of The Companions in Whiterun.

One-Handed Trainers
Journeyman Trainer
Find Amren in Whiterun.

Expert Trainer
Find Athis of The Companions in Whiterun.

Master Trainer
Find Burguk of Dushnikh Yal in The Reach.

Archery Trainers
Journeyman Trainer
Find Faendal in Riverwood.

Expert Trainer
Find Aela the Huntress of The Companions in Whiterun.

Master Trainer
Find Niruin of The Thieves Guild in Riften.

Smithing Trainers
Journeyman Trainer
Find Ghorza in Markarth.

Expert Trainer
Find Balimund in Riften.

Master Trainer
Find Eorlund Gray-Mane in Whiterun.

Stealth Skills Trainers

Sneak Trainers
Journeyman Trainer
Find Khayla at the Khajiit Caravans.

Expert Trainer
Find Garvey in Markarth.

Master Trainer
Find Delven Mallory of the Thieves Guild in Riften.

Lockpicking Trainers
Expert Trainer
Find Majhad at the Khajiit Caravans.

Master Trainer
Find Vex of the Thieves Guild in Riften.

Pickpocketing Trainers
Journeyman Trainer
Find Ahkari at the Khajiit Caravans.

Expert Trainer
Find Silda the Unseen in Windhelm.

Master Trainer
Find Vipir of the Thieves Guild in Riften.

Speech Trainers
Journeyman Trainer
Find Revyn Sadri in Windhelm and Dro’marash at the Khajiit Caravans.

Expert Trainer
Find Ogmund the Skald in Markarth.

Master Trainer
Find Geraud Gemaine of The Bards College in Solitude.

Alchemy Trainers
Journeyman Trainer
Find Lami in Morthal.

Expert Trainer
Find Arcadia in Whiterun.

Master Trainer
Find Babette in The Dark Brotherhood Sanctuary.

Light Armor Trainers
Journeyman Trainer
Find Scouts-Many-Marshes in Whiterun.

Expert Trainer
Find Grelka in Riften.

Master Trainer
Find Mazir in the Dark Brotherhood Sanctuary.

Magic Skills Trainers

Alteration Trainers
Journeyman Trainer
Find Melaran in Solitude.

Expert Trainer
Find Dravynea of Kynesgrove in Eastmarch.

Master Trainer
Find Tolfdir of the College in Winterhold.

Conjuration Trainers
Journeyman Trainer
Find Runil in Falkreath.

Expert Trainer
Find Phinis Gestor of the College in Winterhold.

Master Trainer
Find Falion in Morthal.

Destruction Trainers
Journeyman Trainer
Find Wuunferth the Unliving in Windhelm.

Expert Trainer
Find Sybille Stentor in Solitude.

Master Trainer
Find Faralda of the College in Winterhold.

Enchanting Trainers
Expert Trainer
Find Sergius Turrianus of the College in Winterhold.

Master Trainer
Find Hamal in Markarth.

Illusion Trainers
Expert Trainer
Find Atub in Largoshbur in The Rift.

Master Trainer
Find Drevis Neloren of the College in Winterhold.

Restoration Trainers
Expert Trainer
Find Keeper Carcette at the Hall Of The Vigilant and Colette Marence of the College in Winterhold.

Master Trainer
Find Danica Pure-Spring in Whiterun.

You can only train five times per level, it's hard to get enough gold. Anyone know a good way to make money?

There's a beggar in Windhelm that can train pickpocketing.