You should disenchant them. You can do this in the My Collection screen. This will give you Arcane Dust, which is used to craft new cards.
Note that there is a button allowing you to instantly disenchant all the cards you don't need. That button treats golden cards separately, so don't be afraid if you like to keep them.
A small precision about disenchanting (thanks Kim Minseo) : you shouldn't use disenchanting to exchange one card for another, since it only gives you between 12.5% and 25% of the card's crafting cost, depending on its rarity.
- Common (white) cards cost 40 dust (400 for the golden version) and give 5 (50)
- Rare (blue) cost 100 (800) and give 20 (100)
- Epic (purple) cost 400 (1600) and give 100 (400)
- Legendary (orange) cost 1600 (3200) and give 400 (1600)
What is also worth noting is that sometimes, a patch may change the behavior of a card ; then, for about two weeks, disenchanting it will give its full value. Hence, you might want to only disenchant when you want to craft a specific card, and when cards are worth their full value.