The most long-standing community of longturn gamers can be found over at
LongTurn.org, where there is a basic introduction. Truth be told, some (minor) parts of that introduction are no longer up to date, but most of it is. The basic gist is that you register for an account, sign up for a game that is currently in planning, confirm your participation shortly before it starts and then, once it's running, connect to it from your Freeciv client. Note that the rulesets used on LT are, at their core, based on the civ2civ3 ruleset.
Now, there aren't currently any games that you can directly sign up for (LT42 is being planned, but doesn't have a page in the system yet), but for LT44, which is about to start for real, you might either be able to still get included, or you might be able to replace an idle player in a few days (once the game has started and it turns out some players haven't shown up). For either of those things, you'll want to read and post on the LongTurn.org forums.
The alternative to all of this is in the form of the (new and rebuilt)
Freeciv-web. This is an entirely different game format with way more players (akin to an MMO), where players can join at any time later during the game (albeit probably at a disadvantage), i.e. the games aren't properly planned as on LT. Also unlike LT, it uses (a slightly modified version of) the multiplayer ruleset (notably with double movement).