IMPORTANT FOR PC: Download GlovePie and modify your keyboard bindings because the default settings svck on PC.
These are the settings I use (since i use the arrow keys)

Key.A = Keyboard.LeftShiftKey.R = Keyboard.NUMPAD1Key.F = Keyboard.NUMPAD7Key.Q = Keyboard.NUMPAD4

If you have a specific skill you want to know how to raise, let me know and I'll test some stuff for it.

This will be a work in progress as I go.

!NEW!
Smithing:
Go from town to town buying all the iron ore or iron ingots you can. Likewise, gather or buy all of the leather you can to make leather strips. When you have a ton of leather strips and iron ingots, make a ton of daggers.

!NEW!
Enchanting:
Collect or buy a ton of really crappy soul gems. Walk around with soul trap in one hand and a 1h weapon or spell in the other. Kill as much as you can and just capture everything's soul. Use the soul gems to upgrade the daggers you created while raising Smithing.


Restoration:
Wear wizards robes and get hit by the swinging axes in a dungeon and constantly heal yourself.
(Wizards robes will give you 50% faster regen... even faster if you take the restoration feats)
Just sit there and heal yourself as you get hit by the swinging axes and step back when your health is to low.
!UPDATE!
Raising restoration in this way will leave you with a ton of diseases. Make sure you have a cure disease potion when you are done.


Weapons:
The best way I've seen if you don't actually want to go out of town is to take the conjuration feat to summon for 50% less mana, then wear wizard robes for the extra regen and summon your familiar. When it appears just whack it until it dies. Rinse and repeat. Be sure to take the restoration feats to have even higher mana regen.

NOTE: Your familiar will give you a disease which will lower your weapon damage... this is good for training, but make sure you will be able to remove the disease afterwards.

Armor:
Just get a crowd of baddies on you and just sit there and heal with your favorite armor type on.

Anyway, back to the game

I will check up on this post every few hours.

I'd say the weapon trick is true for any offensive skill, magic or weapons.

For sneak: sneak everywhere. I haven't noticed a decrease in run speed but I've gotten sneak level ups while I thought I was completely alone. Sneak attacks also raise your skill this time around. I've gotten sneak level ups while in mid combat.

Yea, there are a few skills that will be difficult no matter what you do. I'm still wanting to test if you can raise sneaking while invisible though. Then you can just go into a crowded place and get tons of sneaking skill while invis.

i am worried about levelling too much non combat stuff compared to combat. so Ithis guide helps.

I just can't bring myself to attack my breton familiar, though.

Ya, this game punishes you for leveling up non-combat skills too much. Enemies will level up regardless of whether you click the option to level up or not.

Updated smithing, enchanting, and a note on restoration training.