How do you convince the average web user to switch to a non-IE browser?

You need to show them one unique feature that they like and find useful. It could be a plugin/extension.

I'd suggest you say it's good practice to have the latest software installed. And in the case of Internet Explorer - if they are using Windows XP - then they ought to try an alternative - as the latest is not available for their platform.

A lot of people just don't put the time aside to learn how to use or understand their tools. I have a relative that has been using the web for only a year. And they get hung up on the most simple of things. Remember your first experiences? Computers are not that intuitive for a beginner. A little training is invaluable.

Once people are let loose on the web - it's hard to reel them back in.