Your orchid is in its infancy, and that would have been its first flower. Now it has faded, it will need a rest. Cut off the old stem as close as you can to the base. It needs to be in a see through pot so the roots get some light, they won't like being in the dark. They are usually sold in clear pots. Now the flowering is over, you need to feed it with orchid food (most garden centres, instructions on the label) Your orchid will do well on a north facing window ledge - they hate direct sunshine, and spring is just around the corner.
Watering needs to be done thoroughly , but MUST drain straight through the special bark based compost - I do mine on the draining board. They need then to be left for ages before you water again. NEVER let them sit in water as the roots will rot.
The plant will rest for a while, and then it will start to grow new leaves. Don't expect the next flowers until it has formed at least four more leaves - one pair at a time. After that it will produce another flower spike.
Enjoy your orchid.
