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Two basic check:

  1. IP check
    First, you need to check if your IP is the same as VPN server using various online tools, e.g. whatismyip, google etc.

  2. DNS leak check
    Then, you need to use dnsleaktest.com to check if you have DNS leaks. All the DNS servers should be servers of the vpn service or in the region of the vpn server. It should not contain your own vpn services and display your own region.

There are some other tools e.g. port detecting or webrtc checks. But basically the two above.