I got Cool Edit Pro 2.0 and I don't know if it's different on other versions....
Look at tha part on Cool Edit where you work on, if there is nothing that says Track 1, Track 2....Than go to View>>Multitrack View...Go to File>>Open Waveform...Than find tha beat and click Open...A small window will pop up and say that it's reading "blah blah"....After tha beat is opened it should be displayed on tha left side in that box...You can left click and drag tha beat into Track 1 or right click on it and click on "Insert into multitrack"...Than you can go to "Open Waveform..." again and open up your vocals and put them into track 2 and set tha vocals up by left clicking on tha vocal block in tha multitrack and placing it so your words fall into tha beat right (If you right click on tha thin green sliding bar at tha top you can zoom in or use tha magnifying glass at tha bottom left to zoom in and accurately place your vocals)....And for recording in Cool Edit Pro, you can click tha red "R" box to tha right of tha track your going to record into and than clicking tha red-circle record button at tha bottom to left to start tha recording...To edit your vocals you can right click on tha vocals block in tha multitrack and click on Edit Waveform and it will open you up to where you can only see tha vocals waveform...You can do any vocal editing from there if you want...

You might already know that but for mixing everything down just go to Edit>>Mixdown to file...>>and than click All waves or selected waves...And it should open up into tha single waveform with tha mixdown shown...Than just click Save as....and save it...

Hope that helps and can give you an idea of how to work Cool Edit Pro...Just mess around with things and you should get used to it...