I fear the answer is "it depends", both on how you're editing the video and also what/how much "cleaning up" you have to do. If you're editing in Premiere Pro, then it's very easy In Premiere there's a command Edit/Edit in Adobe Audition that will send all the files to Audition in the correct tracks. Once you're finished, in Audition you can use File/Export to Premiere Pro to send it back. Alternatively, if the video editing is finished, you can Export to Adobe Media Encoder straight from Audition to whatever format you want. If you're editing is not in Premiere, my suggestion would be to finish your processing then File/Export/Multitrack Mixdown to get the whole sound track in one stereo (or mono or 5.1) file. You can then import this wave file into whatever editor you're using. If you give more details of how you're working, I can try to be more specific. As for the processing, the same applies. There's not a "one size fits all" solution to offer. I suspect that you may want some mix of noise reduction, compression, EQ and normalising but without knowing more about your project and what you want to do with your sound, that can only be a wild guess.
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