I cut the dead head off but I take some of the stem with it to encourage new growth. if there are several flowers [in a cluster] I remove them individually until the last one then I follow the stem down and cut it cleanly with secateurs.

welcome to GoY too :o)

Look at the stem and find the first outward facing bud below the flower head.
This doesn't necessarily look like a bud, it can look just like a leaf joint. Cut just above it, sloping the cut outwards if you can. If this makes no sense to you just cut above an outward facing leaf several inches (probably 4-6") below the dead flower.

I cut them down to the next 5-leaf set on the stem.