Plug your computer speakers into the computer's sound card. In this case, large speakers with high wattage and subwoofers are preferable, because the speakers should be able to exceed the volume of the singers' voices. Laptop and other portable speakers are certainly too quiet, but medium-to-large standard computer speakers should be sufficient.
Determine the available inputs on your computer's sound card. Most standard sound cards contain a 1/8-inch microphone jack. If you can plug your microphone directly into the jack, then do so. Otherwise, you will need to purchase an adapter in order to plug the microphone in.
Gather the karaoke tracks you want to sing. Karaoke tracks can be found from a number of sources. For example, individual songs and entire collections can be purchased through websites such as Amazon in a variety of formats. If you order karaoke CDs or download files in a karaoke format such as .KAR or .LRC, you will need karaoke software to play them. KaraFun and Gosing are two free options that play many karaoke formats. Alternatively, there are free karaoke tracks available for streaming on YouTube and elsewhere on the Internet. The best way to find them is to search for the name of the song with the word "karaoke" or "instrumental" added to the end.
Configure the sound by accessing your computer's audio properties. This process will be unique to the operating system installed on the computer, but the basic idea is to access the audio properties, enable the microphone and adjust its volume while speaking or singing into it so you can find a level that matches the volume of your karaoke tracks.
Turn up the speakers, load your karaoke player or streaming video and try a test song or two to confirm that everything is working properly. It may be helpful to try singing and listening in different areas of the room to verify the sound is acceptable throughout.