First of all, welcome to Orchid Board.
From your description, I'm guessing that you have a phalenopsis (aka phal, moth orchid). Though they may bloom for months, the floral display will eventually end for the season. Sounds like your orchid has simply come to the end of its bloom life. The flowers fall off & the stem will eventually dry to a twig. Simply cut off the drying bloom spike at the base. Your plant will grow a new bloom spike in due time, probably once a year, though it may turn out to be a re-blooming hybrid in which case you have a happy bonus.
You would do well to read the thread "The Phal Abuse Stops Here". It is quite long, but well worth the reading as it will cover a multitude of problems & answer most of your questions.
Again, welcome.