Cut it as far back as you are comfortable with. It is dead and will not produce flowers again.
Your orchid is a Phalaenopsis Orchid. It is an epiphyte, normally grows on a tree in the jungle for support.
We have wonderful "informational threads" within the Orchid Forums on this site.
Basic care: bright windowsill, no sun light at all, 60-80 degrees, water well when the orchid media(soil substitute) is dry, perhaps every 4-5 days. DO NOT POT IN SOIL! SOIL WILL KILL IT.
Your is looking a bit ragged because in all likelihood it has been neglected.
I strongly urge you to read the thread on Supermarket Orchids within the Orchid Forums. It is full of great information on growing Phalaenopsis.
