Welcome to the forums, here is a http://images.uesp.net//c/c4/Fishystick.jpg for you.
I am looking forward to this new system. I am a bit worried because it's like Fallout, where each level up you pick a new skill, but I believe it's like a TES game where you "use it" you get experiance for it and then level up. How many level ups you need, nobody knows. We are guessing 10 since it was like that in Morroiwnd and Oblivion.
I just hate, I hit someone enough times and when I level up, my lock picking becomes better even though I enver picked one lock at all.
One thing is know a high skill contributes more to levelling up than low skills, not the other way around. Going from skill level 5 to 6 will give you les “xp” than going from skill level 90 to 91.
On the other hand it’s far easier to raise novice skills than expert ones in Daggerfall, Morrowind and Oblivion. I assume this is still true but that you still level up faster raising high skills instead of low. Going from alchemy 5 to 6 might require you to make 2 potions while going from 90 to 91 require that you make 30 potions but you get 20 times more “xp”.
The only way to increase a skill is to use it or probably skill books and trainers. Levelling up does noting with your skills, however you select perks and they does not have to have any connection to the skill you have used, you can make potions to you level up and select a weapon perk, who might give you an power attack but does not increase base damage, next time you use your sword a lot and level up, now you select an alchemy perk who give you more ingredient from plants, again it does not make your potions stronger but you can make more.