The Quake soundtrack was composed by Nine Inch Nails. Trent Reznor and Chris Vrenna worked on it, Charlie Clouser and Danny Lohner probably too, Robin Finck probably not. NIN were working closely with id Software, they had access to work-in-progress builds of Quake. American McGee was responsible for coordination 1).
Apart from the blasting distorted guitar riffs in the opening track most of the music is dark, deep and evil ambient.
There are no official titles for the tracks. Titles that can be found on several websites around the internet were all made up by fans.
Since the soundtrack is standard redbook audio on the CD you can simply put the disc into a CD player and listen to it. The first track on the CD is the data track of the game data which might sound like noise if you try to play it in a CD player.
Each map in Quake has one music track specified to be played when it is run. For example the start map "Introduction" uses the CD track 04. You can see the mappings on Quake's Episodes and Maps.
The various options to buy and Download Quake online do not include the soundtrack, leaving the customer missing a significant part of Quake's atmosphere. You can download a Ogg Vorbis rip of the music at quake_music.zip
Some Quake engines support the use of standard audio files like Ogg Vorbis or MP3 for the soundtrack. Both the Recommended Quake Engines do. Consult their documentation.
If you have the CD in the drive (or a disc image in a drive emulator) but Quake does not play any music, typically the problem is that on Windows or DOS Quake expects the CD to be in the "first" disc drive. So you need to have that drive have the "highest" letter, eg. if you have 2 CD drives D: and E:, Quake will use D:.
Playing in the opening demo of Quake this track can probably be considered a theme song. Noisy guitar riffs and agonizing screams at first, but later it is just distant calm droning.
This track plays during the intermission screens. Rhythmic and weird.
Electric buzzing, incomprehensible whispering, constantly growing in energy until noise guitars riffs come for a climax and then it gets calm again.
Hard evil noise in a breathing rhythm.
Deep beats with a very high pitched chirping.
Like footsteps on frozen snow, a hard and cold rhythmic beating.
Eerie blowing, whining sounds with vague hints of humanity.
High pitched whistling.
Windy hissing noise.