Best place to find servers (if you don't feel like digging for pickups in IRC or on forums) is
http://www.quakeservers.net/
QuakeWorld servers:
http://www.quakeservers.net/quakeworld/servers/
non-QuakeWorld:
http://www.quakeservers.net/quake/servers/
You can get the server's address from those lists, and then connect directly to that address using the Quake console or multiplayer menu.
Or if you use a modern multiplayer-focussed Quake engine like ezQuake (for QuakeWorld) or ProQuake (for non-QuakeWorld) then they will have a server browser included in the menus.
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For bots, see
http://steamcommunity.com/sharedfiles/filedetails/?id=123626484Post edited December 18, 2015 by Johnny_Law