The Dirty Bomb communities have been expanding like crazy in the last few weeks and continues to impress so far. This includes the competitive community ofcourse. Below I will post some links and matching descriptions on where to find things if you're looking for them.

The Main Community Sites
The official Dirty Bomb forums hosted by Nexon, you can find pretty much anything here if you go to the right sub-forums. Patch notes can be found here too(they still haven't figured out how time zones work so beware if you're planning around maintenance/patching xD). There are of-course also recruitment threads for teams here but I suggest using the Dirty Cups forums if you're looking for more serious players, also asking around is a much better tool to get in the 'inner circle' as those teams all know eachother and know if teams are looking.
Self-explanatory to most. The Dirty Bomb sub-reddit. Everything from patchnotes to 'i hate the game threads' and Pro player flame to tips and tricks. Far more complete than the Nexon forums but keep in mind that you also have to dig through more trash. Moderators are generally helpful and fair.
The official Splash Damage forums. This is where the Devs are most active and if you have a serious bug or technical issue I suggest going here with your report/questions. This is also the place where the more competitive players tend to hang out ;). Ofcourse Dev posts/info and patch notes are almost always posted here first.

Competitive Community
By far the most active and prosperous competitive scene is found here. They run a weekly cup on Sundays which combines both NA with EU and you can find scrims on their website if you are not yet familiar with other teams on for example steam(I will admit I don't know how actively used the Scrim Finder is, but from what I've heard people use it :P). This is the best place to find more serious teams if you are team/clan-less so make your recruitment threads here. They also host a mumble where you can enter for PUGs and if your team is desperate for a team VOIP channel you can find it there for free as-well. The PUGs do have a couple of rules so I suggest asking for those when you first join their mumble(the rules are explained in the channel comments but ask if needed). The info for the mumble is:
Port: 64738
Evaczone was one of the pillars that starting the competitive scene way back in the early Beta(even Alpha if I remember correct). After a few unfortunate set backs this site has become a bit inactive but from recent news it seems they are looking to get back into the action soon so keep an eye on them if you want.
Every competitive players knows who ESL is. ESL has hosted a small competitive event and according to United Kingdom Pansy ESL is definitely keeping an eye on Dirty Bomb and it's potential but it's not confirmed if they will be picking it up. Currently there is not much going on there but keep an eye on it for future stuff!
CyberGamer has made a page for an Australian(region locked I think, not sure) DB 5v5 Ladder. Having in mind that this ladder is still not playable it's good to see that the options are getting ready. So Aussies from CF get in touch with those peoples if you're looking for a team, from what I hear the community is small but very fierce(kinda like it was in ET! :D)

Regional Communities

There are numerous regional communities popping up everywhere. I suggest asking around on the official DB forums by Nexon for what is available for your region. Keep in mind that Russia is in a separate client/region so players from that region might have to find other places to do things as I wouldn't be able to tell you where to find stuff.