Loading screen showing level progress bar
To raise your level, increase any combination of your skills multiple times. To increase a skill, use it repeatedly. The lower the skill, the faster it increases from use. The higher a skill, the longer it takes to increase.
Increasing higher-value skills levels you up faster. You can check how far you are from raising your level by looking at the bar on your Skills Menu. The same bar is shown on the loading and transition screens.
When your level increases, you must choose whether to increase your Health, Magicka, or Stamina. You also gain a perk selection, which you can use then, or save for later.