First, way back in the Fall, plant your tulips en masse. This way, if you cut some to grace a vase on your kitchen table, or favorite person's bedside, you will still have enough to be enjoyed in the yard.
From my experience, when you cut the tulips, you usually don't get another bloom. We do have some second-bloom tulips this year that have an additional bud coming up but it is much much smaller. Tulips do better in climates with longer freeze spells than we get here in North Carolina. But we have had great success so far. One thing I've learned is don't listen to everything you're told about gardening. Except here, right?
I digress. Cutting your tulips. I took some photos of the tulips in our garden right now. Cut them while the buds are still "tight" not opened up where you can see the stamens inside like the photo below.
Also, wait until the bud shows its color. Below is a tighter bloom that would be perfect for cutting.
I would give this one another day for the color to become more evident before cutting.
One of my favorite things about tulips is their ability to keep growing taller in the vase after being cut!! So allow for this when choosing your vase.