Also, sneak ... everywhere. It will make progress a little slower, but sneaking is a great way to train and doing so will increase your movement speed when not sneaking as well as agility I believe.
As far as training weapons and other skills, there is a bit of a shortcut I can advise you on.
Go find a goblin town and sneak around until you find a lone goblin guard or child or something.
If they have a weapon, and you have decent wrestling skill, disarm them (wrestle, grab weapon, shift-I for complex interaction, then grab the weapon) and then set your combat mode to wrestle and hold ground.
Sit or lay down (s) and let them beat on you for a while.
This will train your toughness, your armor, and your shield if you have one.
Once you've got really good armor and toughness and agility, you can train weapons similarly.
If you have a weapon equipped without a shield, find a lone opponent with a weapon (preferably a blunt weapon) and lay down in front of him.
As he attacks, you SHOULD parry his attacks with your weapon. This will raise your weapon skill quickly, far quicker than actually attacking him.
Other tips: You can equip more than one item to a slot usually, so, if you have two shields, equip them both in the same hand, that will both double the skill at which you learn shield as well as double the defensive increase.
My other tip is to train throwing on EVERY adventurer you ever make. Even if you are a swordsman, train throwing, gather some small rocks, and every time you get into a fight, start it off by throwing some rocks to soften them up. ALso, if they run away, you will have a recourse instead of just chasing around after them.
The most important advice to any new adventurer though is this: Run away. If it is at all possible, and you aren't certain of victory; Run like hell.
Hide behind a tree and sneak then fast travel away. It'll save your tail, and you'll live to fight ... okay, well you'll live to die another day, but, at least it'll be a different day!