in the loading screens it mentions that melee only levels up when you hit somthing, the same with archery and destruction. but conjuration levels up when you cast it and when, for instance an atronach kills somthing your level will increase.

my question is, is it the amount of damage or the amount of hits that count to leveling up.

I believe it's just amount of hits. I haven't noticed it increasing more when I do more damage/ have op gear at a low level. It seemed to take me just as long as leveling up with no epic enchants and such.

It levels on a per hit basis. Conjuration levels when cast in the presence of an enemy. You can stand on a rock, out of reach from a wolf or even a Slaugerfish, and cast a bound weapon and level Conjuration.

So you can level faster by cranking up the diff to master and using iron weapons.

Higher HPs on enemies + lower weapon stats = more hits = faster leveling.

I guess when you hit you get XP then you level up after a certain amount

This.

i'm pretty sure that block and heavy armor level quicker when you get hit harder, i leveld the last 10 levels of block in five minutes with a giant, it took twenty+ hours of regular play to raise it to 90

Leveling up weapons is per damage not hits.
Leveling up block goes by how much damage you block.
Armor is the same way the more damage your armor absorbs thae faster it will level.
I don't know so much about the magick.

You are certain?
It seems to me, from testing with weapons while, still in Helgen, just the opposite. Maybe I need to reevaluate this...

Source?

UESP I don't know how to provide a link but if you look under leveling,scroll down until you see a list of skills.
To the right under one-handed it say 1 base xp per raw damage dealt.It says this for two-handed also.

Under block it says 1 base xp per raw damage blocked and 5 base xp per bash.

For both light and heavy armor it say 1 base xp per raw damage recieved.

So this means you gain more skill level for more damage dealt,blocked or recieved.

I stand corrected...

From the UESP:

EDIT :

So, given regular gameplay, do you actually level faster on Master?
The enemies have 50% more health, but you deal 50% less damage.

I would think that you would level faster given that you will have to deal 50% more damage to kill a single opponent.
On adept level you would have to find another opponent to inflict that 50% more damage too.

I can confirm this. According to my own testing, using a better weapon requires fewer hits to level up. According to this wikia article, only the base damage of the weapon matters for leveling up. If that is the case, using unimproved high level weapon and not wearing fortify damage enchant would be best. This does not contradict my testing. http://elderscrolls.wikia.com/wiki/One-Handed#Leveling_One-Handed

I went from adept expert, and I definitely noticed how much faster I was leveling up.

You can also level up by increasing skills such as speech, and other non-combat skills like it.

However, if you level up using such skills, your combat ability will not increase. The NPCs will also level up with you, but their combat abilities do increase - this means they'll do more damage, etc., compared than before you/they leveled up.

Good luck.