One of the advantages to using a mastering engineer is getting an objective set of ears to listen to your material and polish it. For many musicians who have sweat blood and tears to write and record songs, it may be hard to step back and objectively listen to their mixes and master them. Having said that, it can't hurt to try.
The actual mastering process should begin with the mixing process. Don't dither your high resolution audio files down to CD quality in the mixes; that should be done as part of the mastering. Don't apply effects like compression and EQ to the whole mix; apply them to individual tracks. When listening to the mixes, pay careful attention to whether any tracks have clipping or distortion on them; that should be fixed before going to the mastering process.
An important part of the mastering process involves using compression and limiters, as well as loudness maximization, to get the overall volume level of the mix high while retaining dynamics. Many pop music mixes are mastered so that all dynamics are removed for the song, setting it so that the volume is just under clipping level for the whole song. While that can make it sound impressive on the radio or in .mp3 format, it does rob the music of the swings that make it interesting and is fatiguing to listen to.
There is no magic formula for balancing dynamics; it comes down to your ears. Compression reduces the distance between the quietest passages and loudest passages of the song. A maximizer will raise the overall level of the mix to a level set by the mastering engineer, and EQ can help boost or trim certain frequencies that are overloaded in the final mix.
The final step in the mastering process is to take all of your tracks and create a CD. Care should be taken in choosing the order of the tracks. There is no magic art to this; again, it comes down to your ears. After assembling the tracks into a CD order, burn it to a CD and then listen to the CD in multiple environments, such as a home stereo, a car stereo, a computer and a boom box, to see how it sounds. The goal should be to get it to sound good on all of these. You may find that you need to remaster parts of the disk, adding fades or reducing fade times, and adding extra moments of silence at the start or end of each track, to get it finally ready.