Oblivion has a unique leveling system in that when you level up so does everything else. Every goblin, rat, and bandit gets stronger every time you do so be careful when and how you level.
How to level up
Leveling up is not based on experience points like most RPGs (seeing as how there are no experience points) it's based on skill ups of your major skills.
At the beginning of the game choosing those major skills intimately effects how you level, when you level, and how many times you can level. Once you have 10 skill points gained you level up. They can be distributed among your main skills in any way, but minor skills don't count.
Maximizing each level
Every time you level you have to choose three attributes to raise. Endurance is always a good choice, but other than that it's based on your style of play.
Some attributes have a +1, +2, +3, +4, or +5 next to them (+5 is the maximum, you don't get any +6, if you've played to up the level of a skill by 12 points). These are bonuses that are based on which skills increased. For example if you gained 8 skill points in block and then level you will have +4 bonus points in Endurance. This means that when you choose endurance to level up you'll get a +4 bonus for one level instead of +1 bonus or nothing. You'll usually do this without knowing, but to create the most powerful character you'll need to carefully maximize your bonuses each time you level.
The best way of doing this is to exercise minor skills. If marksmanship is a minor skill and you gain 10 points in it then you have +5 bonus points in agility yet you're no closer to leveling. Using minor skills in this way is crucial to getting the most out of every level.
Pay attention to the governing "Attribute" per skill and be careful or else you'll level up all of your minor skills too fast and still not level up in a way that will make the game satisfying to play.