In server.properties Edit The "motd= Server" And Make It Whatever You Want
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If you are the host of the Server, you open up Minecraft Server . Wait for it to load then it will say its ready. If you are going to someone else's server, and it has no bars, then there server is not active. (Which means they dont have Minecraft Server up).
Why would you make a minecraft server to play on it urself? It wastes RAM and time.
It does not cost anything to get a minecraft server. You simply download the Minecraft_server.exe from the minecraft website download page. Then, you run it to make your own server.
Type in 'minecraft server hosting' on google, and you'll find a ton of hosts for your server with tutorials.
To make your Minecraft server open for the public, make sure that your white-list is off. Then you will want to go to minecraftservers.org , and register for an account to submit your server IP.