If whitelist is enabled on your server all you need to do is open the folder which contains your server and find the whitelist text file and type their names into that. You can also white-list people by opening up your "minecraft Server Launcher", and type in the text box, (whitelist) (add) (username).
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Some servers have a "whitelist" that you need to be on to get into the server. These are also called private servers. To get onto a whitelist, you need to contact the people in charge of the server and ask them to add your minecraft name to the whitelist. If they do, you can now connect to the server by using the IP.
You will need an admin on the server to add your name to the whitelist. This can be done by changing whitelist.txt or using the command /whitelist add (name)
Just type in "whitelist add <player>" (remove the ").
My server is purely vanilla, small community but it is whitelist.
You set up a whitelist server, and only whitelist the person you want to play with.