I have found that unless you are getting error messages in Windows relating to sound, the only two things that could be wrong are 1) the speakers aren't working, or 2) sound has been turned off.
To check whether the speakers are working, try plugging them into something else that plays sound such as a portable radio/cassette/CD player or a stereo system with a 1/8" headphone jack. Also, you could try your stereo headphones plugged into the computer (be sure to plug them where the speakers go into your sound card, NOT into the CD-ROM drive, for example). If the speakers don't work on something else, or if the headphones do work in the computer, you need to check the speakers. Otherwise, check the sound settings on your computer.
First of all, make sure all the speaker wires are plugged into the proper places. If your speaker has its own power adapter plug, make sure that's plugged into a working outlet. Speakers come in three basic types: those that are powered by the sound card, those that require their own power source, the those that can be switched for either one.
If the speaker can only powered by the sound card, make sure your sound card is capable of amplifying the sound! Some sound cards will provide two out jacks, one which provides power to the speakers (usually called SPK or SPKR) and one which doesn't (usually called LINE OUT). Make sure this type of speaker is plugged into the SPK jack.
If the speaker requires its own power, make sure the A/C adapter is plugged in and working (you can check whether it's working by feeling the transformer; it should be slightly warmer than room temperature), or if the speaker uses batteries, make sure the batteries are fresh and inserted the right way.
If the speaker can be switched, make sure the setting is appropriate for the type of power you are using. Usually the switches will be marked AMP, or it may simply be the ON/OFF button. The switches should only be ON if the speakers are powered by a battery or A/C adapter; if your speakers are powered by the computer, the switches must be turned OFF and the speakers plugged into the LINE OUT jack of the sound card.
If you aren't getting sound from a DOS program, or if sound is missing from one Windows program but all others are ok, check the manual for that program's sound settings. You're on your own.
In Windows, there are several places to check the sound. For the system beeps and the start/exit music, go into the Control Panel, then go to Sounds, and make sure sounds have been enabled and that a .WAV file is selected for each event. Also, most sound card software will include a sound mixer program. Check the settings there (consult the sound card's manual for directions) to make sure the sound hasn't been muted and that the volume is turned up for .WAV sounds.
If it's MIDI songs you are missing, again check the sound mixer, then go to Control Panel and look at the MIDI Mapper. The mapper should be configured to use the FM Synthesizer (maybe Base or Extended). You can double-check the configuration for each MIDI channel by pressing the Edit button. If the mapper is set to the MIDI port, you aren't going to get any MIDI music at all unless you have a piano keyboard (or other MIDI instrument) attached to the computer.
For users of Windows 95, things have been fairly standardized so it's easier to tell you where to look. On the taskbar, next to the clock, should be a picture of a speaker. If that has a 
on it, guess what that means? Click the left mouse button on the speaker icon to check the mute control and the master volume. Double-click the left mouse button on the speaker to check the individual mute, volume, and balance settings for WAV sounds, MIDI songs, CD music, etc.
There are two possible causes for this, one of which is that the volume control for the CD has been turned down (see the preceding paragraph). The other is that the audio cable going from the CD drive to the sound card is either broken or not plugged in at all.
The latter problem most often occurs after installing or replacing the sound card and/or CD drive. However, if that is not the case and you have already checked everything else, it couldn't hurt to check this too. You will have to open up the computer case to check this wire.
Look at the back of the CD drive. There should be three groups of wires plugged into it: a flat ribbon cable which carries digital data from the drive (including sound on program CD's), a set of four colored wires - two black, red, and yellow - for power, and a small set of two or three wires for audio. The other end of this last set of wires needs to be plugged into your sound card; the connector for it will usually be labeled "CD" or "CDAUDIO" or something like that. If the cable is plugged in properly at both ends, check the length of the cable for any broken wires.