This is the end of the season, and I suspect that nothing is wrong, the stem was the first to open and it is done. Cut only the stem (spike) that the flowers were on at the bottom, but don't do anything to the leaves.

I agree with Richard's post. The flowers won't last forever and will fall off sooner or later. I am not sure what "leaves" you are referrring to. The flower spike itself may have sheaths that protected the flower buds and look like leaves. These you don't keep since they will also turn yellow and fall off.
Essentially, the answer to your question is: you can cut the flower spike at the base and discard it, but don't do anything else to the plant itself.

Thank you so much for your response. I guess this is really basic stuff I don't know. So then I have a few more questions if you don't mind:

1. Should I cut the spike after all the flowers fall off?

2. I water my orchid every week and 1/2...do I continue this after all the blooms fall off?

Thanks for all your help!

Your experience with these orchids will really go better if you search for a concentrated resource of information on orchids in general and cymbidium in particular. I'm sorry that I do not have any links to suggest, however, your first question was actually answered by the last poster, to wit, "Essentially, the answer to your question is: you can cut the flower spike at the base and discard it, but don't do anything else to the plant itself." Your second question actually begs more questions: where do you live, where is the cym (indoors or out), how large a container, etc. If you get from that that the answer to question number two is "it varies" you would be correct. But, I have to think that a week and one half is too little water and that might be the cause of the flower death. That said, the cym will only use the proper amount of water when given the proper amount of light. This is all but impossible indoors! People do it all the time of course but not by accident, so we'll need the particulars if you want to know whether you are on the right track or not.

H

I personally cut the flower stem off after all the flowers have fallen off. Some people say it's better for the development of the new pseudobulbs if you cut the flower stem off 4 weeks after the last flower bud has opened but I am not sure if it really makes that much of a difference. Like Howard, I think that watering every 1 1/2 weeks is probably too infrequent. There is a great site' "Phil's Orchid World", http://www.angelfire.com/or3/orchidsnz/culture/cultureframe.html that tells you how to care for cymbidiums month by month. Keep in mind that this guy lives in New Zealand, so you have to adapt his suggestions to your conditions. The website of the Orchid Society Council of Victoria (OSCOV) is also a good source of information. Again, keep in mind that most of the areas in Victoria, Australia are frost-free and provide us with great conditions to grow cymbidiums outside and these websites therefore don't cover growing cymbidiums inside the house in winter, which is what you have to do if you live in an area that experiences frost.
Good luck with your culture and hopefully you will be able to rebloom your orchids.