Guide
How to Kick a Player From Your Minecraft Server
Kicking disconnects a player once. They can join again right away, so for anything serious use a ban or the whitelist.
Kick from the console
Open Console while the world is online and type, without the slash:
kick Namekick Name Take a break, to add a reason.
Kick in game
As an operator, type /kick Name. See How to OP players.
Keep them out
To keep someone out, add them on Players → Banned. To allow only friends, use the whitelist: You are not whitelisted.
Want to try this on a real server? Campfire is free and runs Vanilla. Village adds plugins, Kingdom adds mods and modpacks.