For instance, to level from level 1 to level 2, you require 100 experience. Leveling a skill to X will give you X experience towards your next level. 'Experience' in this case is earned strictly through skill ups. There is a linearly constant amount of 'experience' required for each level.
Level 81 is the maximum level in Skyrim without making any skill Legendary It is possible to repeatedly make a skill legendary or to make multiple skills legendary, this allows you to (slowly) unlock all perk points.
Be warned: You lose all the benefits of having a higher skill level! The advantages of making skills legendary are:
This resets the skill to 15, gives all perk points invested in that specific tree back.
If you have a skill at 100 you can make it 'Legendary'. Since patch 1.9 there is no maximum level anymore.
