Look for a project out on sourceforge that might need help in testing and contact the development group that way. It would probably be the easiest way to find ap roject to help on. I am sure any of those projects would be more than happy to have someone involved to dedicate what time they can to testing.
Insanity: doing the same thing over and over again and expecting different results
Depends what you mean by "work" as a beta tester. You can certainly volunteer to do beta testing.. I see lots of companies and open source projects looking for beta testers all the time.. they will sometimes include perks like a complimentary license to the software.
But if you are looking get paid and create income doing beta testing, I have never heard of that.
You could probably volunteer for one of the many open source projects on the web (such as Mozilla or something like that), but ultimately, that will show only that you're willing to do so. I'd still think that your best bet would be to look for a junior position first and try to work your way back in from there. How much experience did you have before your 3 year break? Were you working doing something else? These are things that might be important to a prospective employer as well.