There are some excellent answers here. I'll add my approach.
I select a research paper that is relevant to the project/area I'm looking a PhD candidate for. Relatively entry level difficulty. I give the candidates a week to read the paper and during the interview I ask a few questions:
What problem is discussed in the paper?
Why is it important?
I think this problem is more or less insoluble. But here are some things I look out for:
I always ask candidates to give a 5 minute presentation about a research project they have done. While there is a risk that this bias' against students who have had fewer research opportunities, all accredited degrees in my field should include a capstone project with ...
Disclaimer: the following answer assumes that the prospect student will be working in a "collaborative" environment.
As stated in the comments, having the certainty that the chosen student will be the right one is impossible.
That being said, I think that the main purpose of these live interviews is not to assess the quality (in terms of skills, ...
When interviewing candidates for industry jobs, I concentrated on two issues:
Is the resume accurate, or if inflated how much? A resume is a sales document, and candidates do try to present themselves as favorably as possible, but it should be fundamentally truthful.
Can the candidate discuss technical issues in the relevant field?
Everything else is ...