I've recorded something on my computer but want to pass it to someone else to work on (they also have Adobe Audition). How do I transfer the files?
Depends upon how large the files are. Very small ones you can email, but this rapidly becomes impractical, and often impossible. One of the better ways to transfer files is to use a service like Dropbox, which will give you secure remote storage that it's easy to upload to and download from. Adobe also has a service like this, but I find Dropbox to be a lot easier to use. It has different user levels but the basic level is essentially free (although at that level it doesn't give you much in the way of control facilities).
As far as Audition itself is concerned, then there are a few other considerations. If your colleague/friend is going to do a decent job, then it's uncompressed wav files (or the equivalent on a Mac) files that you need to transfer - don't send MP3s, which are compressed. These lose quality every time they are opened and saved, because they have to be re-encoded. This goes for any form of lossy compression, but doesn't apply to formats like FLAC, which are lossless. Wav files don't have this problem at all. If you have created a session as well as some audio, then you need to send the .sesx file for it with the audio. The most sensible way to do this is to make sure that the audio you used in the session is in the same folder as the session file itself, so when it is re-opened, the audio will be where the session file expects to find it, and it won't all have to be relinked. Relinking is of course possible, but if you can avoid the need for it, that would be good.
Most of the work I do either comes in or goes out like this.