There are two possibilities - 

1. You can leave them in the flower bed or lawn so that they will re-grow and flower every year (naturalization).  It is important not to cut down the leaves too soon as they are needed for the plant to nourish the bulb for strong flowers the next year. Let the leaves die back naturally. They can then be cut to the base if you want to tidy up the bed.

Note that many of the new hybrids of both daffodils and tulips do not flower very well after a couple of years. This is particularly true of tulips. Our NYBG guide Long Live Tulips has recommended varieties for for longevity. Old varieties of daffodils, such as King Alfred, come back each year quite reliably. Our guide Daffodil Delight has suggestions for bulbs that span the daffodil season. 

2. You can lift the bulbs and store them if you want to plant something else in the same location. Again, the leaves should be allowed to die back before the bulbs are harvested. After lifting, let the bulbs dry out in the sun and remove any remaining soil. Store in a cool, dry location until the fall.  

Having said all this, for the best tulip blooms it is probably better to plant new bulbs every year.

Courtesy of NYBG Plant Information