Well, I've never copied records on to a computer, but I have copied casettes, and the process is almost exactly the same.
As Sparda posted, you will need an rca cable, and an RCA to 1/8" stero jack converter.
Audition IMHO seems a bit overkill.
I use two nice little programs, aptly named rec and wavsplit, to record from a tape and then split the resulting file for burning to a CD. I honestly don't know if these programs are available for ms-windows, and they aren't exactly "point and click" if you take my meaning.
If you are running windows, I'd recommend you check out dbpoweramp (sorry, forgot web address), which will do the job nicely.
~psi42