There are lots of method that canbe used to detect that the user is using VPN.
Already I am seeing lot's answered posts but I want to also give these list what I found on the internet that are used to be detect that people are using the VPN.

• Database validation
• Time zone mismatch
• Transmission Control Protocol (TCP) /IP Detection
• OS mismatch
• Port Scanning
• WebRTC IP address leakage
• DNS IP address leakage
• Latency Test
• HTTP/Proxy Headers
• and many more...........

You will found more details here I would like to suggest you read this article to understand how VPN could be detected an why the sites are using it and also the Conclusion of it.