If I were interviewing a software tester, I'd be most interested in finding out their level of general computer knowledge. This is because the more experience and knowledge they have of computing in general, the more understanding they will have of how programs work and the potential problems to watch for. This knowledge is usually only cemented in someone who has an active interest in computers and spends a lot of their spare time using one. The person who only started using a computer in college or only uses one when they have to is not usually very knowledgeable about them.
To kick off I would ask general questions. Did they have a computer growing up, or frequently use one? Do they know what basic hardware components are in a computer and what their respective functions are? Do they understand what an operating system is? I would not hire someone who floundered about at this level.
If they are going to be testing internet applications, I would also check for some general knowledge about the Internet. What is DNS? What is a router? Do they understand client side (browser) versus server side processing? Lack of knowledge here wouldn't be an automatic fail, but it would leave serious doubts in my mind.
I would gradually get more detailed in my questions, especially if the candidate expressed that they are experts or very knowledgeable in a certain area.
My third approach would be to test their problem solving skills. Your QA tester might not be fixing the bugs in the code, but the more they can narrow down the problem and identify the specific circumstances that trigger it, the faster and cheaper it will be for your developers to correct the bug. To do this I would present some sample problems and ask the candidate how they would proceed and report the bug. Presenting an actual live demo on a PC would be ideal, but hypotheticals would work as well.
And finally, I try and see how methodical the candidate is. The ideal candidate is going to approach testing methodically - he / she is going to be able to create a testing checklist / method which will cover all the important aspects of the program's functionality thoroughly. This is a hard one to test for. You may pick it up while posing the hypothetical (or real) problems to the candidate, and watching carefully how they proceed.
If you are running the interview, and don't really have good knowledge of the above areas, try and get someone who does to interview, or the smooth talking candidates will easily pull the wool over your eyes and impress you with their confident ignorance. If you are that potential candidate, and you know you are not very competent in any of the above areas, save yourself and any potential employers a lot of pain, and take some career aptitude tests to find your true career path.