There are a few ways to level quickly (without "cheating" - at least without entering console commands) eg:
If your a stealthy type character get yourself the mage guild recommendations sorted asap (kind of a must anyway) so you have access to the enchanting alter. Make yourself some chameleon armour then go find a guard by a gate, point at the wall next to him (find a corner if you can), sneak, tap q (autorun) and point in the corner. Leave the game to its own devices for a couple of hours and instant level 10 character (so long as stealth was a major skill ofc).
Lots of other things like this you can do. Eg acrobatics:
Jump in the water next to imperial city and find a corner of rock you cant walk onto (eg a bridge works too) again, point into a corner and leave it swimming for a couple of hours = lvl 100 acrobatics and level 10 character.
Using the 2 above would give you a VERY good stealthy type char.
Find some armour of your chosen type (light or heavy) get a shield enchant on it so you take less damage - go find something small that is unlikely to kill you (eg mud-crab) annoy it and leave it to hit you punatively for a few hours, lvl 100 armour and 10 character levels.
You get the idea - theres LOTS more, there all kinda slow but good to get a decent character level. Only trouble would be that some creatures would get massively powerful against your rather feeble combat skills. So mebbe something to do after a few levels done the normal way
Currently have a lvl 30 kajit sneaky type with a decent array of spells to back him up. Also means I can enchant some pretty evil spells onto weapons (e.g 2 sec paralyse and 50 drain health on a decently meaty weapon)