The Steam Game Servers API provides everything you need to create dedicated servers for your game. You can host these game servers yourself, or allow your community to host them for you. This is the best choice for highly competitive games (such as Dota 2) or games with persistent servers that stay around after players leave (such as Team Fortress 2).
Steam Server Browser
A large part of the the game server experience on Steam comes from the unified server browser.
Players can open the server browser from the steam client or in the Steam Overlay
You can get the same data as the server browser with the API functions available in ISteamMatchmakingServers
You can get and interact with the users favorite servers with:
Shipping your game server
If you want to allow your community to host dedicated servers then special considerations may have to be taken when giving them access to the dedicated server files.
See: Distributing Your Dedicated Game Server
for more information