I've never grown broccoli myself however I found this - so I hope it is helpful.
The edible part of broccoli are compact clusters of unopened flower buds and the attached portion of stem. The green buds develop first in one large central head and later in several smaller side shoots. Cut the central head with 5 to 6 inches of stem, after the head is fully developed, but before it begins to loosen and separate and the individual flowers start to open (show bright yellow). Removing the central head stimulates the side shoots to develop for later pickings. These side shoots grow from the axils of the lower leaves. You usually can continue to harvest broccoli for several weeks.
Full article is here: http://www.urbanext.uiuc.edu/veggies/broccoli1.html