If this is a Moth Orchid, a Phalaenopsis, then cut the finished flower stem back to just above the bottom node up the stem (a little scale on the stem).

It should produce a new stem either from the node, or from between the leaves.

If it's a Paphiopedilum, leave the stem for a while - some are sequential flowering and may produce further blooms from the stem. Cut if it starts to wither as close to the base as you safely can.
Dendrobiums and orchids from the Oncidium alliance (these are commonly marketed as Cambria in the UK) will not reflower from a spent spike, and should be cut off. These benefit from a period of rest (cooler temperatures and reduced watering) after flowering and through the winter.