Summarize:

If someone is lying to you, there's a good chance that electronic proof exists. People often log their locations and activities on social media. Texting and instant messaging also make up a large portion of person to person communication. If you can gain access to someone's phone or social media account, you will likely know who they are talking to and what they have been doing. Think long and hard before you go snooping around in your partner's digital accounts, though. What if they aren't lying? Are you going to lie about doubting them and invading their privacy, or come clean? If you believe someone is lying about where they are going, you can find out with a simple stakeout. Go to the place that they claim to be and keep yourself out of sight. Watch closely to see what time they arrive, what time they leave, or if they were even there at all. If their story checks out, they were telling the truth. If not, you have proof that they were lying to you. You may want to hire a professional (such as a private investigator) if you might need proof for legal proceedings, such as evidence of infidelity for a potential divorce. Also, stakeouts aren't as easy or as fun as they might appear to be on TV. If you suspect someone is lying to you, you can always ask other people they know. You can ask bluntly ("Were they really with you last night?") if you are comfortable doing that. If not, you can try to get the information you need through casual conversation ("Did you two have a good time last night?"). A skilled liar will try to concoct a good "cover story" for the people you're likely to ask; but those people may not be good liars themselves. If you've built up a strong case that the person isn't telling you the truth, go ahead and confront them directly with the evidence: "I'm sorry, but your story about what you did last night just doesn't add up, and I'm confident that you're not telling me the truth. What really happened?" The person will either finally come clean, fumble around trying to build another lie around the old one, or get upset that you don't trust them. If you're worried they'll respond poorly, wait until you're both calm and composed before confronting them. If the person is a compulsive liar, don't assume that catching them in a lie will cause them to change their ways.
Look for digital proof. Conduct a stakeout. Verify their story with friends or family. Confront the liar.