Go in to your Minecraft folder (%appdata%\.minecraft), then open the saves folder.
In there, all your Singleplayer worlds are saved.

Now select the Singleplayer world that you want to use for your Multiplayer Server, and drag it into your Minecraft Server folder.

Now, you will already have a folder inside of your Server folder called world. You'll have to delete it.
After you have deleted the world folder, you can rename the Singleplayer world folder (that you dragged into the Server folder) to "world".

Restart your server, and you're done.

Going off a more specific route than creeperkid09's answer.

You need to make a running server first before you move you're singleplayer world to the multiplayer Server. If you have already done that skip down past this next bit.....

Server Set-up

Download the newest Server file from http://www.minecraft.net/download once you have done that, move it into it's own folder (doesn't matter where the folder is as long as you remember where you put it.) and rename it to minecraft_server. Then press start and open up a new Notepad and type the following into the notepad...

java -Xmx1G -Xms200M -jar minecraft_server.exe nogui
pause

Next you save the notepad into the same folder that the Server File is in, and name it "Run.vbs" and under the name there should be a drop box, set it to "All Files" Then click Save. Next, you run the Run file. after it is done creating a few files open the EULA Notepad found in the server's folder, and change false to true press Ctrl and S to save it, then close the notepad. Then double click the Run File again. It should generate the rest of the server files then once that is done...

Server Set-up Done.

Delete the folder names "world" in the server's folder and move your singleplayer world into the server's folder and rename it to "world" all lower-case. Then run the "Run" file and the server should start up.

You will need to use Hamachi to have your friends join, or you can port-forward. But Port-Forwarding is more dangerous.

If you have any trouble with any of this let me know, I'd be happy to help you with this. I had the same problem not too long ago & I couldn't find all that much help.

Skye assumed you were using a PC, if not then refer to a video by minituff (hamachi free mac server hosting). As for turning a world from single player to multiplayer just rename your singleplayer world to 'world' and put it in the server folder.

http://www.minecraftforum.net/forums/support/server-support/tutorials-and-faqs/1940466-how-to-create-a-minecraft-server-easy-guide

Go through that step by step and you can make a multiplayer server.I'm taking a guess that this is for pc Minecraft.

Making a server takes ages and if you are not sure about it then do not do it as hosting a Minecraft server and port forwarding can leave your computer open to anyone.

If you wanted to connect with someone who is connected to the same internet as you then press 'esc' then 'open to LAN' then just get the other person to connect to the ip 'local' and that should work.

Making a Minecraft server takes a long time and consumes your computer usage so a good computer is reccomended for this.

You could pay for a server by just googling 'minecraft server hoster' some good ones include 'Creeperhost' 'mcpro host' or 'netherbox' all good, reliable and safe hosting companies require you to pay via different plans for different kinds of servers, more information will be on their respective websites.

Sorry for such a long answer but I hope this was enough information ;)