To easily gain experience use the "Easy gold" glitch to get lots of gold. After you save Arl of Redcliffe's life, a soldier will appear in your camp with a box for donating money to the army. You will gain experience for each donation you make.
In Lothering, run to the right upon exiting Dane's Refuge to find a quest giver by the name of Allison. She will ask you to make three traps for her and reward you with a moderate amount of experience and 50 Silvers. Take advantage of this as the quest is repeatable and will no longer be exploitable as you progress in the game. To do this, go back into Dane's Refuge and purchase Trap Triggers. He has an infinite supply of them. Assuming you have Trap Making, create Spring Traps, which only cost approximately 3 Silvers to create. She wants 3 per turn in so it only costs you roughly 9 Silver for the quest. She will reward you with 41 Silvers profit per turn in, not to mention the experience that comes along with it. Note: Take advantage of this exploit because Lothering will be unavailable to you at various points in the game.
To gain more experience points earlier in the game, go to Denerim as soon as you leave Lothering and find a building named "Wonders of Thedas". Go inside it and purchase the Archivist's Belt. As long as it is equipped, you will get an experience point boost for everything in your Codex. For instance, books will increase from 50 experience points to 75 experience points.