Buy mixing and mastering software such as ProTools, Cubase, Adobe Audition and Audacity. Audacity is freeware, so you can legally download without paying a fee. Adobe Audition is also offered as a mastering software. Other mastering software includes Sound Forge, Peak Pro and Wavelab.
Connect speakers to your computer. You won't want to mix through headphones. You will also want to mix in a room where sound does not reverberate much. A small room with lots of cushions, furniture and drapes to absorb the sound works best.
Make sure you have all of your instrument, vocal and audio tracks recorded into your session. For more control over the sound, you'll want each instrument and vocal to be its own track. As you edit the tracks, compress them so that the peak levels are consistent without obscuring the sound. Kick and snare will need a lot more compression than vocals.
Start editing drums in this order: kick, snare, tom 1, tom 2, cymbals. There should be two cymbal tracks. Apply a noise gate to the kick, snare and toms. A noise gate will remove the excess noise so that all you hear is the sound of the instrument that you recorded on that track. For the kick track, all you will hear is the kick drum. For cymbals, apply a high pass filter. A high-pass filter reduces the amount of low frequencies on the track. Pan your cymbal tracks hard left and hard right. Pan tom 1 a little left and tom 2 a little right. Leave the kick and snare centered. Add a little bit of room reverb to the drums to liven them up.
Edit your other instrument tracks. Leave the bass guitar centered and bring up the high frequencies on it. Don't use reverb for the bass. The electric guitar can be panned left or right however much you decide. If you record two tracks of the same guitar, you can pan one left and one right to make the guitar sound like it's in an arena. Add a little reverb and bring down some of the low frequencies. For rhythm guitar, apply a high-pass filter and pan hard left or hard right. Leave synth pads stereo to fill the song out. You will want to leave them in the back by adding reverb or keeping them quiet. However, synth leads can be loud and treated the same as lead guitar.
Edit your vocal tracks. Your main vocal should be centered and cut through all of the other sounds in your song. Add reverb and delay to liven up the vocal. However, be careful when using these effects because you don't want to lose the vocal. Apply a low cut filter to reduce low rumble and popping Ps. For female vocalists, you may need to use a de-esser to get rid of harsh Ss and Ts. Do the same thing for harmony; however, harmonies can be panned left or right. If you have more than one harmony, try panning one left and the other right. Be careful with reverb and delay on harmony. You don't want the harmony to smear with the lead vocal.
Play the song through and listen for instruments or vocals that need to be turned up or down. Vocals will usually need to be turned up. Cymbals need to be quiet because they will pierce through a track. The bass needs to be very audible to fill the track. Depending on the style of music you are mixing, you will need to adjust certain options. For instance, a hip-hop or dance song will have a lot more kick and bass than an adult contemporary song. You will need to listen through the song and make adjustments several times.
Mixdown the song to WAV or AIFF file. WAV files are more common for PC and AIFF are more common for Mac.
Bring the song into your mastering software. Equalize the song so that it sounds the way you want it. You may need to turn up the highs and lows. You shouldn't have to change the song drastically. Compress the song. The song should peak out at 0db. If you have to, normalize the song to 0db.
Listen to the song. If it sounds the way you want it to sound, save the file. If not, go back through and make further adjustments, then save the file. Your song is now completely finished.