General quests, picked up from NPCs across Tamriel, can give you lots of experience. You get this not only for completing the quest, but also for killing the enemies you encounter along the way! More demanding quests will give you a higher amount of money, so don't only go for quick and easy quests.
 Guilds are back in the installment of the Elder Scrolls, so take advantage and complete the guild quest lines. The various quests you pick up can give you an easily laid out way to get XP, helping you level faster by creating a clear path of things to do.
 Since battling is the real way to gain XP, what better way can there be to gain it than to participate in a full-scale war? Once you reach level 10, you'll be allow to participate in the war effort, fighting for your home Alliance (and later, switching sides if you want to). This will net you loads of XP, depending on the size of the battle and how much you participate.
Do general quests.
Do guild quests.
Fight in the faction wars.
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