you pick. this will encourage the bush to make more flowers. if you don't, the plant will put a lot of energy into making rose hips, which contain seeds. if you remove the heads, the bush will make more flowers to try to make more seeds.
watch out for bees! i got stung by a bee who was sleeping inside a flower. it really hurt for a couple hours.
you only want the petals, not the leaves or hips or stems. it should be easy to separate the petals from the rest of the flower as you are picking them.
if you have time to make rose water now, you can use fresh 