I have a reputation at my job for being notoriously good at reading people. At first I got some shit for it, but now the owner of the company takes my opinions seriously. If he finds out I dislike or distrust someone, he will immediately call me or schedule a meeting if he's in town. It's kinda cool, but also can be a burden.
There are the classic things
However for me it primarily comes down to two things; intuition and attention to detail. When people lie/are hiding something they tend to overlook minor details of their story.
Recent example - Colleague A is stressed one morning at work, and confides to our desk clump that it's because she thinks she's pregnant and is leaving early to go to the doctor. Colleague B wants another kid (yet can hardly take care of the one she has, but I digress) and is clearly jealous. She immediately asks A if she would consider giving her the baby. B also tells A that ultrasounds are painful (wtf?) and that her 6 week ultrasound left her in tears. It turns out that A is pregnant and rises to the occasion. A few weeks later, A makes a comment about missing margaritas. B tells her it's perfectly safe to drink during pregnancy and that she drank a lot because didn't know she was pregnant with until her second trimester.
Yet she had an ultrasound at 6 weeks. It was fun calling her out on that!