Getting Cymbidium Orchids to Bloom?

Orchids thrive on neglect, so don't over water. They also like a shady spot. I would trim off the old flower stem, and wait and see. I got an orchid that some one had thrown out. I fed it with a liquid fee that contains no copper, and suddenly it was in bloom. They do take a while to re-bloom once the blooms die off. I water once a week a good soaking.
Most nurseries and garden centres will stock fertilizers for orchids. There are two kinds, one kind to stimulate growth and the other is formulated to stimulate flowering.

It has a higher proportion of potassium. If you over water it you will get a lot of yellow leaves and a sick looking plant. Most orchid potting mixes have a high content of bark and are very coarse, the water will generally go straight through. After a few years in the same pot its a good idea to repot the orchid and this will sometime stimulate more flowers. Good luck.