I've just downloaded the most recent version of CCleaner. I have not used that program in many years, so I'm rusty as to how to approach running it.

I've run the "analyze" part of the program, and a list was generated. Are these the items that will be deleted when I run the "cleaner", or will other files, etc also be deleted? I'm assuming that it's safe to let the program delete the items on the list it generated, yes?

Let CCleaner "clean" away. It's original name was "Cr*p Cleaner" because that's what it gets rid of - all the junk left over from daily use. I guess they got so popular that they "cleaned" up their image!

It doesn't touch any documents or programs. It is very thorough and will get rid of any cookies you haven't excluded from it. I keep several cookies excluded from the cleaning such as Gameboomers so I don't have to log in again. Just click on Options and then Cookies... move the ones you want to keep over to the right side. If you want to do that before you click on Clean, you will have to start over.

I'm a little confused: Since I've "analyzed" already, if I move the cookies I want to save now, I'll have to "analyze" again, and then go to "clean"?

Yes, that's right. The first analyze included all cookies.

I use two parts of CCleaner :

First Registry/Scan for Issues
Which I always click to be fixed once they are listed, if any DO get listed

And then Analyse.
I always click for any items on this list to be deleted.