finally stopped blooming

[doolee25]

We received a beautiful orchid as a gift. There is no identification of just which orchid it is. I had about 4 blossoms and several buds. All of the buds have blossomed, and what is left is a healthy looking stem and just as healthy looking roots. It in a 6" plastic pot. I would like to know just what I need to do to have it blossom again, How long before I can expect to see buds? The only instructions were to water with three ice cubes once a week. Do I continue that protocol? We live in central Connecticut, and the plant is in a North by northwest window. It gets lots of light, but not direct sunlight.
Any suggestions for a complete novice in orchid cultivation will be welcom.

Thank You