You can try and it is still worth it, but success is not guaranteed. Since Fall is already upon you, it is best you do this indoors.
The first thing you will need is medium. You can use compost or rooting gel. Other options are also available, such as mixtures of soils etc., but if you are new to this, trying compost or gel might work okay.
If you are using rooting gel, that they sell in some stores, you don't need to add rooting powder. If you are using compost or a soil mix, then you ought to consider using rooting powder to encourage growth.
If using rooting gel, they usually come in convenient containers, so you can just use those. If not, just get a small cup, like an 8oz or a 12oz coffee cup sized one. Fill it with your compost. Wet it, but make sure water does not log at the bottom.
Cut off the flower, because if you have the flower up there, the cutting is going to expend all its energy in keeping the flower going for as long as it can.
Dip the very bottom of the stem into rooting powder gently and then lift your stem and stick it into compost. Make sure it is able to stand, if not support it with a stick (if you buy orchids, they usually have a support bamboo stick with clips for support and you could steal one from a dead orchid) and a clip or rubber band.
Cover this with a ziploc or similar bag to help keep the warmth locked in. The bag has to allow light to penetrate. Set this up against some bright, indirect light and wait for about 4 - 6 weeks.
Just cautioning you again, trying to propagate store bought rose stems is more likely than not, to fail, so be prepared. There is also the potential that at least some of the roses are patented, and you can't resell it even if you rooted it and it grew well.
Your best bet would be to show us pictures, we can get you close to an ID, and then as spring starts up, you can go to a local nursery or online and order a nice bare-root bush and plant it in a pot or your garden and enjoy the results, but, if you are willing to experiment and try your best, why not? I am always trying to propagate plants I can lay my hands on...