There are two basic categories of speakers for quality monitoring from a computer: studio monitors and high-end computer speakers. Studio monitors are designed for music recording. They tend to have flat frequency response and give you an accurate representation of the sound. High-end computer speakers may not have as flat of frequency response, but may sound more exciting in the low-end and mid-range frequencies. Also, consider if you want stereo or surround-sound monitoring.
Computer speakers usually connect directly to the sound card, while studio monitors will likely require another piece of gear. You can run the output of the sound card into an audio mixer that connects to your studio monitors. For many home studios, a small audio interface is a good option for both inputs and outputs. An interface will connect to your computer via USB or Firewire and will give you audio outputs to which you can connect your monitors. You will have to run specific software in order for your interface to function properly.
Powered studio monitors have built in amplifiers, while passive studio monitors require a separate amplifier. Powered monitors tend to be more affordable, compact and portable, making them a good choice for most computer recording environments. Passive speakers offer more customization and tweaking.
The size of a speaker correlates with what frequencies it will be able to reproduce. A general rule is that larger speakers can reproduce lower frequencies. Five-inch woofers and smaller will have difficulties reproducing frequencies below 100 hertz. Computer speakers often have problems reproducing really low frequencies.
Subwoofers add range to the low end of you monitoring system's frequency response. It is useful to add a subwoofer when you are working with smaller speakers. Many computer speakers come with a subwoofer that also works as the amplifier and distribution unit for the other speakers.
In order to hear a correct stereo image through your speakers, position them correctly. The ideal setup will create an equilateral triangle between you and the two speakers. The speakers should be separated by a distance equal to the distance between your nose and one of the speakers while you are seated in your listening position. The center of the speakers vertically should line up with your ears while you are seated in your listening position.