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
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.
For bots, see http://steamcommunity.com/sharedfiles/filedetails/?id=123626484
Post edited December 18, 2015 by Johnny_Law