Is sound enabled in the operating system? In Windows, the basic "Sounds" menu is found in Control Panel. Sound events that have little speakers next to them are enabled. Enable sounds for some actions that you recognize (like "exit program" or "minimize") and see if your speakers work now. Note that operating system sounds don't need to be enabled for music CDs or games to work, but if you're here, we're starting off with the assumption that you aren't getting any sound out of the speakers at all.
Have you loaded the best driver for the sound card? The best driver means the most recent driver, so check the manufacturer's website for an update, because your sound card may have been sitting on a shelf for a year before you bought it. If the sound is integrated on the motherboard, check for an update at your motherboard manufacturer's web site.
Does Device Manager register the sound card or integrated motherboard audio and report that the device is working properly? Even if you don't have the proper driver, Device Manager will probably identify it as a sound controller. Before you start stripping down the system or chase off to conflict resolution, make sure the adapter is seated in the motherboard slot.
If the Device Manager reports a resource conflict between any of the audio devices and another device, look through all of your device reports and figure out where the conflict is. It may be resolvable by changing the settings in Device Manager, or it may take aggressive reshuffling of adapters. If you get a "!," "?" or "i" on the sound controller in Device Manager, proceed to Conflict Resolution.
Check your documentation or the symbols on the sound card to make sure you actually have the speakers plugged into the proper jack. On high-end sound cards with front and rear speaker jacks, try the front speaker jack first. Check that your audio patch cables are all plugged firmly into the proper jacks and that the cables aren't damaged. If you have USB speakers, they don't jack directly into the sound card.
Software volume controls are the #1 problem with sound, and a real pain to figure out if multiple people use the system. Aside from the primary volume control often found in your system tray, there are various other mixer panels and volume adjustments that get installed with the driver and are offered in various applications. All of these can cause a complete absence of sound if the "mute" box is checked. I don't have any magic method for finding the mixer panel or any additional volume controls in a typical system. The Multimedia icon in Control Panel is a good place to start.
Does your sound system work properly with everything except music CDs? If so, proceed to CD and DVD Playback diagnostics. One good test is to try the speakers and cables on another system, or another device with a speaker jack, like a portable radio. Make sure you first turn the speaker volume control all the way down in case the output is already amplified. If your speakers and cables don't work anywhere, try swapping the cables to find out which is faulty. If the speakers and cables are good, either the sound card is blown or you didn't look hard enough for a hidden mute in software.
If Device Manager only registers the sound card when you strip out all the adapters except the video card, it's definitely a conflict. If you have another sound card lying around, it's a good time to try it; otherwise proceed to Conflict Resolution.
If your only audio support is built into the motherboard, make sure it's enabled in CMOS Setup. If you are using a sound card, make sure any motherboard audio is disabled in CMOS Setup. If you can't get the operating system to recognize the sound card, which is sure to be plug-and-play, shut down and unplug, remove all the other adapters except the video card from the system, reboot and let the BIOS and operating system adjust. Then shut down and unplug again, replace the sound card, and see if you can get it going. If this works, you might still have problems when you add the other adapters back in, but if you do it one at a time, at least you'll find out for sure where the conflict lies.