1. Defective hardware.
If there is a working volume control in Applications Sound & Video ⇨ Volume Control or Applications ⇨ Sound & Video ⇨ AlsamixerGui, or on the desktop toolbar, then defective hardware is less likely. On new installations, the case may be simply that the Master or PCM channel is muted. If no sound card is detected these controls should be "grayed out" and unusable. If the volume controls are missing or disabled (i.e. you cannot move the slider control), you can confirm the diagnosis by following the instructions in the next section, then take the machine back to the shop that sold it to you or seek assistance from a professional.
2. Incorrectly detected hardware.
Whether or not volume controls work, it is worthwhile to check whether and what devices have been detected by Linux. Most Linux distributions should have the command line tool lspci or lshw available, however hardinfo provides a nice graphic interface & report generation. Ubuntu users can install it via the package manager or at the command line with:
sudo aptitude install hardinfo
The menu icon should appear in Applications ⇨ System Tools ⇨ System Profiler & Benchmark but may also be launched with at a command line:
In any case, the audio device will be listed under PCI devices. The reported device should be compared with the actual installed hardware to determine if it was correctly detected. If no audio device is listed, then this is a clear indication of missing or defective hardware.
3. Application Issues
If the hardware appears to be correctly identified and in good working order, the Master and PCM channels are enabled and volumes are set sufficiently high, speakers are plugged in and their volume is also turned up, and you are still unable to produce any sound in any application, professional assistance is probably in order. Those who are brave, foolish, lucky, or eager to learn can poke around online for reports of similar issues, in particular, users of Ubuntu Karmic (or any derived distributions) should check Ubuntu's Karmic Caveats as well as the Ubuntu Multimedia & Video Forums as many users have reported issues related to the Pulse Audio sound server.
If you're still stuck after all the above, your best bet is to seek out your local Linux User's Group where you are sure to find someone willing to help.