Getting someone to own up to a lie is a delicate matter. Most people will feel threatened when you ask them to tell the truth if they've been lying. The best way to do it is with a little empathy and a way for the liar to save face.
Figure out why the person lied. Some lies are malicious, some lies are designed to cover up mistakes or bad behavior and some lies are told with the best of intentions. Knowing why the person lied can help you decide the best tone to take when you talk to him about his.
Ask to talk with her privately, in a place where you won't be disturbed. If she's a friend, family member or an employee, this can be relatively easy. If she's a colleague or an acquaintance, it may be more difficult to arrange this talk without arousing her suspicions. Approach her in a friendly way so you don't make her feel threatened.
Give him a chance to save face by talking about the event or fact that he lied about. For example, you can talk about what you know of the event, showing how it contradicts his version. Then, ask if you misunderstood what he reported about the event. Though he's not directly owning up to the lie, he understands that you saw through it and you've gotten a truthful statement from him. If this occurs, proceed to Step 7.
Confront her directly if she sticks to her lie. Explain that you think she's lied to you, and tell her exactly what leads you to that conclusion. Let her know that you're not going to get angry at her if she explains.
Allow him to explain his lie while you listen. If you have evidence that he lied, he'll likely own up to his lie now. He may have an explanation of why he lied, so listen carefully and empathetically to his reasoning.
Respond to his reason for the lie. If he lied to be kind to someone, acknowledge his good intentions and talk with him about why the lie wasn't a good idea, or at least about why he should have been honest with you. If he lied for a malicious reason or to cover up for himself, tell him that this sort of lie is unacceptable.
End the conversation on a positive note if possible, and thank her for owning up to the lie, or clarifying the situation if she corrected herself in Step 3. If she's hostile at the end of the conversation, stay calm yourself and she'll probably feel better once the embarrassment of being caught in a lie wears off.