You get quests by talking to non-player characters. Walk up to an NPC, make sure your weapon is sheathed, then press F while you target him. This will bring up a dialogue window and depending on what services this NPC offers, you can buy and sell items, train skills and spells, or get quests.

Completing quests for NPCs may unlock new quests.

Some quests are repeatable, and can be done as many times as you want. These are usually kill-quests and some of these may have random rewards, with a small chance for elite rewards.