Well a lot of the scammers want to connect to your computer/phone in order to 'investigate' or offer up some sort of 'refund'. You can keep them on the phone for a little while by just talking to them, however the real time-wasting comes in when you let them run around in circles on your computer. My OH and I are currently working to create a fake bank, so that we can log in and let them think they have us where they want us.
I wouldn't suggest anyone do this, unless they know what they are doing. You should never allow them to connect to your computer or phone - never click on any links they may send you or download any apps. I know that is a given to some people, I just wanted to mention it.