To let your friends join your game, you can simply check the "Allow friends to join" checkbox when going into your single-player game. Your Steam friends can then right-click your name, get game info and join your world. For this feature to work your computer must not be behind a firewall, or the firewall must have UPnP enabled. Most routers do.

You can also launch a stand-alone server somewhere as well. The server executable is ~60 kb, and uses very little resources. Players have been running servers on devices as tiny as a Raspberry Pi, for example.

The stand-alone server executable can be found in the game folder and is called WWServer.exe. To run it on Windows, simply launch it. To run it on Mac or Linux, use mono (may need to install it first):
By default when you launch the server you will be informed of all the parameters you can specify for it, such as "-world WorldName" to load a specific world file, and "-public" to make it public (it will be private by default, meaning you have to give your IP to your friends in order to play). If the server is started as public, it will show up on the list of servers in-game.

It's highly recommended that you create the world first before starting the dedicated server. Create your ideal world in single player like you normally would, then remember the name you used. For example if your world name was "New World", then you'd specify that as the world name when launching the server:
To launch the server with all the parameters easily, create a shortcut on Windows, or a batch file. To create a shortcut, right-click the WWServer.exe executable and choose "Create Shortcut". Then right-click the newly created shortcut and go to Properties. You will now be able to edit the Target field, specifying any additional properties you need. For example, this is the line I use to start the Development server: