I have played semi-competetively over the years in some leagues and lans etc. More recently in house leagues in Tribes.
Pretty much all teams I joined were formed from people I was playing with at the time. Although getting into a voice comms program helps, particularly if there is a community driven base like there was in Tribes. The main Mumble server had all the team channels as well as the PUG channels and public lounges etc. Was pretty easy to find games and chat with people and you take it from there.
Back in the Quake days IRC was the tool everyone used, but these days teams have their own websites and use chat programs like Ventrillo, mumble or Team Speak. They also use social media.
I also joined an online gaming group, primarily for ARMA III called iOGC. Great bunch of guys who set up gaming nights on all kinds of games. Had much fun attempting to play Planetside 2 with those guys! Not really competetive teams or anything but fun all the same.
I suppose it depends on how pro you want to go, but I am confident that if a person wanted to be in a team and play competatively they could do so, even now (if they are good enough obviously!). There does seem to have been a shift, though, and the more common lobby gaming systems become, the more dilute any community gets, or at least the less demand there seems to be for clans.
Personally, I am old school Quakle 3 - Gifford, Barrysworld and Wireplay + IRC some beer and a deck of smokes till 5 in the morning (quit smoking now though!). Job done
Having said that, Tribes Ascend filled a void for a good while, and still does to a degree. I just never get time to play it anymore

C'est la vie