Ok, first off - no you don't need to pay for a server, unless you want a high-end one for a lot of players. When you create your own server from the Create Multiplayer menu, make sure that the LAN box is un-checked. If you still can't see your server online, you need to forward (or "open") some ports on your router so it's visible online. Here's the basics:
1) Type
http://192.168.0.1/ in your browser address bar.
2) If you're asked for a username and password, enter admin as a name but no password and hit enter.
3) Now look for a page / section on the router config screen you're looking at that's called "Virtual Server" (That is most likley the port forwarding page, but every router varies).
4) Now HL2 games require 3 ports open:
Code:
UDP Port 27015
TCP Port 27015
UDP Port 27020
Set those ports so they're open on the Virtual Server / forwarding page and make sure it's for the computer you're using (Usually 192.168.0.100). It might be a little confusing but I can't help you there unless i know what kind of router you have.
5)After step 4 is done, Garrysmod should be visible online!
If you want to make a dedicated server (A server run from a dialog box without you needing to actually join the game), then download this little package:
GMod_Server.zip (708KB) and extract it's contents somewhere. Look at the readme. It will download all needed content for your server. Note that it's a little bit more complicated to run a dedicated server so search the forums a bit about that if needed - but using that little kit is WAY easier than downloading it from
http://srcds.com/
Hope that helps! The rest of you MingeBags just posted crap that didn't help the poor newbie out. *shakes fists*
That little gmod server kit I linked to above originally came from
http://time2burn.org/ but the website has since then disappeared :(