When tulips are done blooming you should dead head them and try to keep the leaves green as long as possible. Meaning water the tulips when soil is getting dry. After the leaves die back you can either choose to dig the bulbs up and divide them or keep them in the ground during the summer. We advise to dig them up at least once every three years.
Why and how to dig tulip bulbs
In Holland tulip growers dig up every year all bulbs they have planted in the fall. After digging they divide the bulbs (A bulb multiplies in 1 big bulb and several baby bulbs). The big bulb they sell and the small baby bulbs they plant again next fall (to grow big bulbs again...) this is how they multiply their tulips.
Video: My dad digging tulip bulbs in 1975. (the little boy is my oldest brother, I was't born yet in 75!)
In your own garden you can do the same. Multiplying will even go faster because you will not sell any of your bulbs...
There are varieties called "perennial" tulips. Those tulips don't multiply as fast and come back year after year without digging them up.
Video: Here I am explaining "How to store bulbs and why some tulips perennialize better" on a live broadcasting show called Virginia Home Grown.
Most people do not know this but Virginia has a pretty good climate to perennialize tulips. It is very important for the tulips to be warm and dry in the summer (in Holland that's not ideal, even in the summer it is rainy and cold. Tulips are always treated as annuals in Holland!).
When the tulips are done blooming you should try to keep the leaves green as long as possible. Water the tulips twice a week when the temperatures are above 75 degrees. After the leaves die back you can either choose to dig the bulbs up and divide them or keep them in the ground during the summer. I advice to dig them up at least once in the three years. To guarantee top quality flowers you have to buy every year new tulips from Holland.