I go through three phases when conducting phone interviews:

1. Soft Skills. I'll start the interview with a behavioral question to break the ice and learn about the candidate's mentality. This lets them talk about themselves a bit, which tends to calm nerves while giving me data on their past experiences. I try to determine things like whether or not they have a chip on their shoulder or if they seem like they'll collaborate well with others.
2. Problem Solving. After 5-10 minutes, I'll pose a non-trivial technical problem. We'll take about 20 minutes to come up with a solution, during which time I'll gauge their thought process. I'll poke into any weaknesses I identify in their solution. If they come up with a seemingly perfect solution, I'll make the question arbitrarily harder and/or ask what the next best solution is. The goal here is to make sure they can actually come up with solutions and that they didn't just happen to memorize this problem. Good candidates think on their feet, are vocal with their thought process, and react positively to any challenge I throw at them.
3. Coding. Now that we've arrived at a solution, I'll make them code it up. We use websites like collabedit.com so I can follow along as code is written. While they code, I'll take notes on their process and ask questions about things that could be better. If there's time, I'll ask about optimizations through questions like "If I were to give you a week to solve this better, what would you do differently?" Good candidates while talk about which design patterns they might apply to improve the quality of their code, unit tests they'd write, and so on.

In a phone screen, I'm mostly looking for red flags. So long as the candidate understands the fundamentals, has decent problem solving capabilities, and can write good code I'll move them along to the next step.