Good list of way to train all your skills
General
You can take back the gold you get from skill trainers by making them your companion, and by pickpocketing it back from them after you get training. For your magic skills, get 100 enchanting, all 5 enchanter perks, insightful enchanter, corpus enchanter, extra effect (extra effect not necessary, so i guess you only need like 70 enchanting). Enchant a ring, necklace, body armor, and helm with -25% [insert magic school here] magicka cost.
Alchemy
Make damage magicka regen, damage stamina regen, invisibility, paralysis, and slow potions. These are worth the most and thus give the most experience.
Dmg mag regen ingredients: Bear Claws, Blue Butterfly Wing, Blue Mountain Flower, Hanging Moss, Nightshade, Spriggan Sap, Glow Dust, Spider Egg, Chicken Egg
Dmg stam regen ingreds: Creep Cluster, Frost Mirriam, Giants Toe (use these with wheat, trust me), Histcarp, Juniper Berries, Large Antlers, Silverside Perch, Skeever Tail, Wheat
Invisibility: Chaurus Eggs, Ice Wraith Teeth, Luna Moth Wing, Nirnroot, Vampire Dust
Slow: Deathbell, Large Antlers, River Betty, Salt Pile
Paralysis: Briar Heart, Canis Root, Imp Stool, Swamp Fungal Pod
My favorites are hanging moss and blue mountain flowers... very easy to acquire and very good exp/value.
Alteration
Cast oakflesh over and over while you are in combat with an enemy who is stuck in the water.
Find the Transmute spell in Halted Stream Camp (North of Whiterun). Mine/buy/steal a lot of iron ore. Use transmute to turn the iron ore into silver ore, then gold ore. Making gold ingots. Make gold necklaces for 1 gold ingot a piece.
Block, Light and Heavy armor
Just go into a cave/mine with a really low level enemy and back into a corner. You can then just elastic-band your block button down. Make sure you set the difficulty down so you don't die.
Or for only leveling block is lure a mammoth, just one, have a Shield out and a healing spell in the other hand (or use healing potions). And just block. Levels it fast.
Conjuration
Buy the bound sword
Find slaughterfish
Stand at the edge of water so slaughterfish can't attack you, and so that you'll still be in combat
Cast bound sword (don't dual sword it), sheath your weapon and repeat.
You can get the Apprentice Conjuration magic perk to make this process go by faster. This process is so quick you can have 100 conjuration in little over 1 and a half hour.
OR repeatedly cast soul trap on any dead creature.
Smithing, Enchantment & Speech
Buy/ mine iron ore/bars.
Acquire leather strips.
Smith as many iron daggers as possible
Acquire gems.
Enchant iron daggers with weak enchantments.
Sell daggers 1 at a time for good profit.
Or if you want to train Speech very quickly.
Go to riften, black brian meadery.
Talk to the guy at the counter, ask him to tell you about the meadery.
Use the persuade option. if it fails, bribe him gold instead, you need atleast 26 speech for persuasion to work i think so if youre not 26 yet, youll only need to bribe a few times to reach lvl 26.
Repeat.
30 minutes later, youre level 100.
Enchanting is very easy to train with the Black Star. Just enchant soul trap for 1 second on a weapon, trap the soul and reaload the weapon using the Black Star. Repeat.
Sneak
Go to the Greybeards (after you are revealed to be Dovakiin) and sneak attack them. Greybeards will attack you if you attack them, but they won't attack you if you attack them with a sneak attack crit, bows would be the best option here.
Or if you have a Brotherhood contract to kill someone, be in a distance where you can see them, go into sneak, then just move back and forth or left to right.
Hadvar or Ralof in Riverwood. Sneak and attack him repeatedly, he will not retaliate nor will you get a bounty. (At Algor's or Hod's house, depending on who you followed out of Helgen).
Illusion
Dual Cast courage for any NPC and Muffle for just repeatedly casting it upon yourself.
All combat skills (Destruction, One Handed/Two Handed)
Put the difficulty all the way up, cast a Frost Atronach spell and wail on it. Or, do the Dark Brotherhood quest to acquire Shadowmere and put the difficulty all the way up and wail it. Once it it enters combat, heal it when it reaches low health then wail on it some more.
Lockpicking
Get a dickload of lockpicks and find a master lock (check out the Dwemer Museum for some high level locks) and continue to break all your locks.
There's a training chest in the Thieves Guild that you can gain access to very early in the quest line, pretty much right after joining. Wait until you attain the Skeleton Key(if you wish to not waste lockpicks) late in the Guild's primary quest line. Just like in Oblivion it is unbreakable, use it on the training chest to achieve results very quickly. Note: You have to give it up to finish the quest, so be sure to exploit it beforehand.
Pickpocket
Assuming you've already gotten a high enchanting level, enchant at least a ring and necklace with fortify pickpocket
go to any town
pickpocket
repeat
the success rate is crazy high with 1 or 2 measly fortify pickpocketing enchantments. Valuable items/things that weigh a lot give the most experience, if you get caught just take the 25 gold fine, dont bother saving/reloading etc. Once youve stolen most of the valuable things in one town, move onto another. More valuable items show up when you have a higher pickpocket.
Restoration
Get a high level ward spell, find a necromancer camp and continue to deflect their spells.