if the stem has dried up it wont flower again from that stem, its dead. You need to cut it off right at the base of the plant so that all that's left is a short stub, you can google exactly where is recommended at the base, there are a lot of really easy to follow step by step tutorials, Ive used them myself but now I usually just cut it as low as the clippers can manage without nicking the rest of the plant and they were completely fine afterwards, Ive even had new stems growing not long after. The new stem might take a while to show up and then grow but once its fully grown the orchid will flower again from the new stem.

Just a though, you could maybe give it a repot too some fresh media does wonders. And you would get a chance to see how the roots are doing. Thus giving it a good shot at being a better bloomer next season. I find that my phals just take off after I repot them. Velleta

Thank you both so much! This has been very helpful and I appreciate you taking the time to tell me.

I will be clipping the dead stems and repotting them, it very well is time to do so.

ps: Those are phalaenopsis. These are from the Philippines and grow more or less in People friendly temperatures. They do, however, like a ten degree drop in the fall to initiate new flower spikes for the following year. Yours look like they are doing just fine. ...and yes, you can cut off the flower stems at the base, once they are done flowering to get a new spike the following spring or, if they are still green, leave them on to get mini-spikes the year round. I prefer the full spikes as they will have more and bigger flowers but a lot of people like to have the year round flowers.

You have received some great recommendations here. Since the orchid already bloomed, you should repot now in fresh media. The best time to repot is after flowering when new roots should begin growing. Phals prefer to be under potted so move up to a larger pot only if there is no room for new roots in its current pot. You might try to tuck the aerial roots into the new medium to see if they'll grow down into the pot. If not, they need to be kept moist by spraying them with water. As noted beforehand, clip the dead flower stems off. If there is a flower stem that has already bloomed and is still alive, you can cut that stem about a 1/4 inch above the last node. This might trigger new growth from the node & a second round of flowering. Good luck!