Dynamic Processing
Dynamic processing can either make your mix shine, or destroy the whole essence and flow of your sound. When mixing vocals a good preset to use in Cool Edit is "RealAudio Compander" (effects>amplitude>dynamic processing). This will regulate the peaks of your vocals and will even out everything so that the audio is even all the way through.
Noise Reduction
Noise Reduction is also extremely powerful when cleaning up a rap vocal, especially if it's recorded poorly. To properly use noise reduction you need to select at least 5 secs of the audio track were no there is no vocals, after this go into the noise reduction tab (effects>noise reduction>noise reduction), in the tab click "get profile from selection" and then click close.. yes close. Once your back looking at the wave file select all (ctrl>a) and reopen noise reduction. Now play around with the noise reduction level slider until you get it to a number where you like how it sounds. Good numbers are
Anything from 55-90, the lower you go the more of the noise you are going to hear the higher you go the more of your vocal presence your going to lose.
Parametric Equalizer
Most of the time vocals need to regain some of the essence and natural sound that they lost during dynamic processing and noise reduction. To do this you need to use an equalizer and parametric equalizer (effects>filters>parametric equalizer) in Cool Edit is perfect. This is pretty much personal preference but most of the time augmenting the mids in vocals will make it sits nicely on the beat and a good preset for this is the Mackie Mid (Boost). Play around with these settings to achieve the sound that you want.
Reverb/Echo
Reverb (effects>delay effects>reverb) is also a personal preference effect; reverb will thicken up the vocals and add a tiny bit of delay depending on how you set it. A good preset in Cool Edit is the "Tight and Close" preset but of course to make your mix really shine is better to make your own original reverb setting. Echo (effects>delay effects>echo) is also a good effect when mixing rap vocals especially in the ad-libs and doubles. Echo gives the mix presence and makes it fun. It is also good to make your own echo preset that is not to echoed but enough so is felt in your mix.
Panning/Volume
Panning is extremely important when you have adlibs and doubles recorded because it gives your vocals body if all these elements are panned precisely. Usually the main vocals are panned slightly right or left (R5 or L5). Doubles are panned right or left opposite to were your main vocals were panned (R20-30 L20-30). And finally adlibs are panned not too much where they can be hardly heard but not to little where they overpower the main vocals. Good adlib panning is usually set between R15-20, L15-20 opposite of your doubles. Volume is also good to play around with in every track, the doubles in rap vocals should always be less so the main vocals don't get overpowered the same goes with the adlibs.
Final Notes
Mixing is simply an art and Cool Edit got powerful effects to make you rap vocals really shines. Training your ear to hear flaws in your mix makes it easier to correct them and playing around with settings is always good to learn what each specific effect does. These set of steps is just a basic way to clean up and mix your rap vocals so that they sit nicely in a mix with quality.