Question: how do professionally recorded and/or mastered audio recordings get that "sheen" or that "glass-like quality" ? Is that something done in the mastering stage, or is it something done during the mixdown stage?
Is it something done with a compressor? If so, how is it done?
There really is no single answer to this question, as the "sheen" or "glass-like quality" can mean different things to different people, and can come from many different sources and stages of the recording, mixing, and mastering process.
I'm going to have to take an educated guess and say that you are referring to how bright everything is mix and mastered these days... i.e., an abundance of high frequencies in the mix. Also, that is also couple with a thinned out mid-range, which helps to make everything sound more clear and open, and lets those high frequencies stand out even more.
It's important to note, though, that everything starts at the source. You've got to have great players playing great sounding instruments to get that tonal quality to begin with. If it's not there, it's very hard to generate it later on.
So, it starts with great sounding instruments and great players! For example, if you want that really glass like strumming quality on an acoustic guitar, you need a guitar that is fairly bright to begin with, and you need to put on new strings (which will sound brighter), and the appropriate weight strings to get the tone you are after.
Next is the recording process... picking the right microphones and knowing where to place them to get the sound you are after, and having a good room, with proper acoustic treatment, to record them in. Again, using our example of an acoustic guitar, if you put a microphone right in front of the soundhole, it's going to sound boomy and muddy. Instead, if you want a bright strummy sound, you need to have that microphone up around the twelfth fret of the guitar and fairly close to the neck, and record it in a great sounding room that doesn't make everything sound boxy and muddy. Also, you would pick a nice small diaphragm condenser microphone to get that brighter sound out of an acoustic guitar.
The next stage is mixing. However, the way you mix things is largely dictated by the arrangement of the song. Part of what makes a great mix is a great arrangement where the instruments compliment each other and are not stepping all over each other. There needs to be enough space in the musical arrangement for each instrument to have its own space, along with room to breathe, and not interfere musically or frequency-wise with other instruments and vocals.
If you've got a great arrangement and everything was recorded well to begin with, then the mixing stage becomes fairly easy and is a matter of simply enhancing things with some subtle EQ and Compression as needed.
If, on the other hand, you've got too many instruments playing at the same time, and a bad arrangement, so that it's become a big muddy mess, and the artist won't let you take out some of the tracks during the mix, then you definitely have your work cut out for you. In those type of situations, mixing becomes a process of trying to make space for all the instruments by doing a lot of "carving" type of EQ, where you take out broad ranges of frequencies from some instruments to make room for others. The mid-range will get muddy really quick, and that ruins the whole clarity/sheen thing, so you end up cutting a lot of mid-range out of a lot of instruments to clean up the mix as much as possible.
Also note that compression may help instruments sit better in the mix dynamically (volume wise), but compression usually has the side-effect of reducing the transients and making everything sound a bit duller, so you'll usually need to add some high-end EQ back in after the compression to compensate.
If everything was done right, and the tracks sound great on their own, the arrangement is great, and the mix turned out great, then the mastering engineer should really only have to do some balancing between overall levels and EQ on songs for the whole CD, and, if you want to compete in the loudness wars, they will bring up the overall volume and brightness a bit to be competitive, and hopefully enhance the overall sheen a bit, without doing too much damage to all the hard work you have done to make everything sound great so far.
However, many times mastering engineers are required to try to repair poorly recorded and mixed music, and they may have to do drastic EQ and other processing to make the song passable.
So, it can really happen anywhere along the lines. Compression certainly isn't the answer and can actually work against you if you are looking for sheen and glass-like quality (most beginners over-compress everything).
What you really need to focus on is getting your instruments to sound the best they can be to begin with, and picking the right microphones and microphone placement to begin with the capture the sound the right way to begin with. The less you have to do with EQ and other processing, the better everything with sound in the end.
After all that, learning how to EQ properly is probably the biggest challenge that most beginners have trouble with. Our ears are easily fooled into believing that anything louder and/or brighter sounds better. So, the beginning starts out by soloing tracks and cranking up the various EQ bands. By boosting EQ, you are adding volume to the track, which always sounds better to our ears. And, as you boost the upper mids and high frequencies you are adding both volume AND brightness, which our ears always think sounds better. Before you know it, you have all the EQ bands cranked way up on almost every track. Then, when you put everything together in the mix, you get a big jumbled mess that is either too muddy, or too harsh, and nothing seems clear or separated.
As a mix engineer, you have to retrain your brain to learn how to EQ without being fooled by changes in volume and brightness, so you can learn what is really working better. It's more a matter of making space for each instrument and doing some subtle enhancements... figuring out the most important frequencies of each instrument and making sure there is room there. That involves a lot of subtractive EQ from other instruments... probably the most important thing to learn how to do in order to clear up your mixes and make everything sound more open and glass-like, without having to crank up the high frequencies on everything.
It's really something you can only learn by LOTS and LOTS or practice and trial and error! You've really got to work on mixing as much as possible and learning how to EQ properly. It's not just a technical thing, it's an art (just like playing an instrument) that you get better at the more you practice.
You may also want to look up an article entitled "3D Mixing and the Art Of Equalization" that I wrote a long time ago and is available in the article sections of this site.
Hope this helps.