Ok, this is a very good question and there are many ways you can do that. I got into software testing from computer networking background. I have done three certifications in networking such as CNE, MCSE and Cisco CCNA. After that I joint a small company as network admin. Working there for 1 and 1/2 year I applied in a mid company for network device driver testing and it worked. One thing I had is a niche skill of Novell Netware admin skill which I got from CNE certification. So if you follow the same path then make sure you have some niche skill say Sun Solaris Unix, Oracle or any other thing. SAP testing is another good option. There are many trainings available on that.
Other way is to become a automation specialist which has got great demand in the market. Take a training of QTP or Rational functional tester etc and complete the certification tests. Then again start in a small company with lower salary (some times not true) and after working there for 2 years (that what I would recommend) go for the big fishes like IBM, Wipro etc.
Hope this will help.
If you need more information feel free to post here and I will try to answer.
Thanks
Raj