You only get five slots plus an ultimate. At level 15 you will get a secondary set along with a second weapon. As you weapon swap you can use 5 different skills and 1 ultimate.

Picking the right abilities is a major part of your build. You can't slot everything you know, so you need to decide what's going to be useful to your build.

Also, notice, that slotting various abilities can affects others stats (if you have the appropriate passives). For example, slotting assassin abilities will increase your weapon crit, or slotting shadow abilities will increase your total health. In some cases, abilities will provide passive bonuses directly. Concealed Weapon (the magicka morph of veiled strike) increases your stealth movement speed by 25%, Flawless Dawnbreaker increases your weapon damage by 8%, and Werewolf increases your stamina recovery by 10%. But, because Dawnbreaker and the Werewolf transform are both ultimates, you have to pick one.

While leveling up, just keep swapping all the different abilities on your bar whenever you turn in quests. Ideally by the time you get to 50 you want to have all the class abilities, armor skills, fighter's guild and most of the weapons leveled up