Host public server
There's very little you need to do in csgosl to host a public server. Under the Server tab just make sure the lanonly setting is not ticked (it is as a secure default after installation). You probably also want to set a password and change the server name which also can be done in the Server tab.
There are however two more things, unrelated to csgosl, you must do to host public servers. The first is to get a Game Server Login Token from Steam. This is a security measure taken by Valve. The second is to setup port forwarding in your router to allow people to connect from the Internet to the server you want to publish. It's fairly easy, just follow the instructions below.
To host a public server, i.e. a server accessible over the Internet, you need a Game Server Account. This is free and can be generated by visiting the Steam Community Game Server Manager. You will receive a game server login token which you need to enter in the Steam tab under gameserverlogintoken.
Failing to properly setup a GSLT may cause various problems as described in this issue. GSLT can expire, in which case they are valid but not working any more. If you just make up up it will (most probably) be invalid and will be handled differently as described in the before mentioned issue.
It's a little bit confusing to read about which ports really need to be forwarded on various forums but these are the ones I forward and it works for me (TCP and UDP for all):
27000-27050
3478
4379
4380
These ports need to be forwarded to the IP address of the machine where you run your server. How this is done depends on the router you use but typically it looks something like this:
Rulename......Ports............TCP/UDP......IP addres
CSGO-1........27000-27015......Both.........192.168.1.200
CSGO-2........3478,4379,4380...Both.........192.168.1.200
(please ignore the dots, just there to keep stuff aligned, yes, I'm useless at HTML...)
In this example the machine you are running the server on has IP address 192.168.1.200.
To get a complete and very good walkthrough on how to do this on your router head over to portforward.com. Select your router in top left menu (you may need to close down a commercial window) and then select the game "Counter-Strike - Global Offensive" and you will find detailed instructions for your router. Here's an example for the Asus RT-AC66U router so you know what you're looking for.
Good luck!