My bedroom light has burned out and I do not know how to replace it, because I do not know how to get this screw thingy off.
The decorative nut has been removed but there is still a small little nut that is holding the little escutcheon up against the glass. Use one hand to hold the glass and try to loosen the nut with your fingers, if you can not get it to move with your fingers try a pair of pliers gently.
There isn't a visible bracket behind the glass. So that threaded pipe likely screws into a bracket inside the fixture at the ceiling, or might even go through the fixture and into a bracket attached to the electrical box.
That nut holds the glass (there is typically a big washer between it and the glass to protect the glass; once you get it apart, you can stick another washer there. There's usually a decorative knob that screws onto the end of the pipe. If there wasn't one, that (and a brass washer if you need one), are common, inexpensive lamp repair pieces that you can find at any big hardware store.
As you're looking at the nut, like in the picture, turning it counter-clockwise should loosen it. If it's too tight to turn by hand, you may need a wrench or pliers to get it started. Pushing up on the glass will take a little pressure off the nut and make it easier to turn. Once you get it loosened a little, support the glass with one hand and turn the nut with the other; the nut may just spin off by hand and then you will already be holding the glass.
If the nut has become stuck to the pipe, the whole pipe may unscrew. Either way, the nut, or pipe and nut, will come off when you turn it enough to unscrew something from something. Don't try to grab the pipe with pliers to keep it from turning; that will damage the threads. It isn't a problem if you end up unscrewing the pipe.
After it's all apart, it will be easier to separate the nut and pipe if they're stuck together. If the pipe has been unscrewed, you can put that back in and then secure it in place with a nut against whatever bracket it screws into. If there isn't a nut at that end of the pipe, you can get them at any hardware store (they're a standard size).
Putting it back together, verify that the pipe is tight in the fixture. Then you slide the glass over the pipe, hold the glass with one hand, stick the washer and nut on the pipe, and get it started by turning the nut clockwise as you're looking at it. It should spin easily. If it feels tight, it means that the nut isn't square against the pipe and the threads aren't aligned. Just unscrew the nut and try again. If you can easily turn it several revolutions, it's on right.
Then hold the glass in place while you turn the nut clockwise to tighten it. Just make it hand tight while you are pushing up on the glass. That will be enough to keep the glass secure; don't over-tighten it. When that's done, the knob goes on the end of the pipe.