After your tulips are finished blooming you should keep the leaves greeen as long as possible.
Keep them well watered, (twice a week). After the leaves die you can either remove the bulb and divide it or leave it until the next season. It is recommended to dig up bulbs at least once every 3 years. One bulb will prudce several baby bulbs so digging and dividing is a good way to multiply your tulips. Keep in mind that tulips need adaquate space and will not grow well if they are crowded so make sure to seperate the baby bulbs and give them enough space to grow.
There are some verieties of tulips known as "perennial tulips". They are different in that they don't multiply as quickly but will come back year after year without any digging.