How do you take care of an Orchid house plant?

Try to identify which Orchid type that you have first, so that you can tailor your attention to best suit it.

The commonly found ones are:
Phalaenopsis – 'moth' orchid
Cymbidium
Odontoglossum

Phalaenopsis have thick fleshy oval leaves. This benefits from good warm conditions. Avoid drafts!
http://www.carterandholmes.com/Merchant2/merchant.mvc?Screen=CTGY&Category_Code=1250-Phalaenopsis

The following benefit from some cooler weather and temperature differential between day and night to encourage flowers – they are typically spring bloomers:
Cymbidium have thin reed like leaves. Can be placed outdoors in summer. Benefit from a 25 degree temp. difference between day and night, in order to iniitiate flowering. Indirect sunlight is best for these.
http://www.collectorscorner.com.au/Orchids/Cymbidium2.htm – look for some of the photo's which show leaves to help ID yours.

Odontoglossum have false green 'bulbs' that sit above the growing medium. Can be placed outdoors in summer.
http://www.collectorscorner.com.au/Orchids/Odonts.htm

These and most orchids benefit from good amounts of light, although harsh direct sunlight is typically best avoided.

All of them dislike standing in water, for more than the briefest of times, which can cause them to rot. I water all of mine by standing them in some soft water, such as clean rain water (better than tap water) for a couple of minutes. I water mine just before they dry out, which means more during the warmer months.

None of them like to be over-fed and you can get specialised Orchid fertiliser, which I use every 3 weeks or so, during the growing season.

Orchids typically like fairly humid environments, and you can manufacture this by standing some pebbles in a saucer of water, near to the plant. This will evaporate and increase the relative humidity. You could stand the plant onto some pebbles, with water not touching the plant base – which they won't like, otherwise, just use a small dish/saucer and leave it nearby. You could even use some of those glass pebbles that you can buy, if you find them more decorative.

You can also mist them, with a small sprayer, to aid humidity, though this is more temporary than having some standing water nearby, all of the time.

It would be helpful if you could say what signs of dieing your plant is showing. No flowers last forever, but if you are getting leaf problems, then consider that it may have suffered some cold whilst it was in transit or storage to the shop/nursery: this won't be your fault. If it's given some tlc now, especially with the better light conditions of spring in the northern hemisphere, then it may well make good strong growth and recovery.

Hope these thoughts help. Private message me if you need more advice, or have problems identifying the type of orchid that you have. Good luck! Rob