I can't figure out how this leveling works! OK, I just started, and got out of the sewers. I went to the island across the way, slew some bandits, explored a dungeon, sold some swag in the capital. I counted more than 10 major skill ups (tdt displays it, too,) but I cannot level up!

I chose Combat, AGI and END, with Blade, Mysticism, Destruction, Marksmanship, Security, Armorer and Illusion. My major skill ups so far are (from tdt: )

STR: Blade 5
END: Armorer 1
WIL: Destruction 1
AGI: Marksman 3, Security 4

Major Skills Advanced 8/10

But... it should be 14/10! Anyone with the wisdom of Uriel Septim, can you help?

Sleep and you'll level up.

All hail Emperor Septim! Uh... I watched you DIE dude.

I remember having about 20 active quests by the time I first went to sleep. I spoke with a homeless person - quest. Talked to a shop-keeper - quest. Picked a plant - quest, When I finally got to sleep, I awoke in the MIDDLE OF THE OCEAN. ON A QUEST.

I was feeling a little overwhelmed by this point. Also overjoyed by the depth of the content,

If you don't sleep you can easily close all the Oblivion gates and probably finish the game too as it seems all the bad guys level with you so they are tough but not that hard to kill.
I was level two (I slept once) when I closed all the gates.

No, no, you don't understand - he is only 8/10, sleeping does nothing. They system thinks that he has only incurred 8 Major Skill gains, but I count 14 (above!) I slept, nothing, no level.

Ok, I think I got it, but I don't know how it is factored. Leveling up in the tutorial, is a little strange. For example, I hit a rat with a rusty axe, and when I get out, all of a sudden my blunt is like 25, when I hadn't tagged it as a major, meaning it should be somewhere around skill level 9 or 10. Skill leveling in the tutorial seems to happen dramatically faster.
It's been a long time since I did the tutorial, I make a save before I leave the sewers and restart characters there. Perhaps not count what happened in the tutorial? I'm reaching here.
Only other question would be, do you have mods?

Are all of these skill-ups since leaving the tutorial dungeon? Some skill advances get changed around when you set your class, and it can affect what's counted for leveling.

During the chargen dungeon, you gain experience points. Since you start with all skills at 5 + racial modifiers, all these experience points net you a lot of skill increases. But once you choose your class, the level ups are erased, you get your class skill and specialization modifiers, and the experience points are redistributed.

So the experience points that amounted to 6 skill increases from skill level 5 to skill level 11, might amount to not even a single increase at skill level 30 that you get after 5 + racial + class + spec.

EDIT: of course, you gain experience points throughout the game as well, not just during chargen. And I don't know why they made it so complicated. I prefer up-front character creation the way it was in Morrowind. Why should my barbarian have a healing spell and fire damage spell? He has an aversion to evil juju magic!

I usually remove that flare spell (I play on PC) from my non-magic characters. You can't remove the healing spell, though, because the game defaults to it if there's no other spell selected.