Getting the Master Server Patch
In order to play online, you will want to get the Master Server Patch.
From that link, install the SWAT 4: Gold Edition version. Do not place the DLL files in the SEF/System folder, or they won't work. If you have already installed the master server patch, you do not need to install this again.
After this patch has been installed, you will see game servers on the Join Game menu. It is recommended that every player install this.
You will need to "open" or "forward" ports on your router. Specifically, SWAT 4 needs 10480-10483 TCP/UDP opened. If you want to use WebAdmin, you will need to open port 6000 TCP also. (Or whatever port you choose in creating the server)
Setting up the Server
Now you will need to go ingame and set up your server, including map rotation, admin permissions and settings, etc. Use the LaunchSEF.bat to launch the game and use Host Game. Now set up your server - including the name of the server, map rotation, and other settings. Make sure to tick "Launch as dedicated server" in the Advanced tab.
Now, once you have adjusted the settings to your liking, you're ready to launch! If your server crashes or your computer restarts for updates or something else, you can use the Dedicated Server.bat to start your server quickly.