(Is there a link that should be here, but isn't? Let me know!)
Block B's official Twitter feed is here, its Daum fan cafe site is here, its Instagram is here, and its Facebook page is here. Seven Seasons, Block B's management company, has a Web site and a You Tube channel. At the moment, Zico’s KOZ Entertainment appears to be using his Instagram. Block B also has a Japanese (日本語) Web site, a Japanese Twitter feed, a Japanese mobile site, a Japanese Instagram account, a Japanese LINE blog, a Japanese YouTube channel, and a Weibo account (Chinese/中文). If you use KakaoTalk, you can add Block B as a Plus Friend, and they also have a channel on V App.
A number of fan groups translate Block B material into a variety of languages. (And a big THANK YOU to all those hardworking BBCs!)
BeeSubs translates into English
BBC Mexico translates into Spanish
Block B Romania translates into Romanian
7BUSTERVN translates into Vietnamese
Block B Thailand translates into Thai (ภาษาไทย)
Block B FAMILY translates into Chinese (中文)
ArabBBC translates into Arabic (العَرَبِيةُ)
There are more international fan groups out there! Block B International has a list of fan groups by country, so look there.
If you want to try puzzling out the Korean Tweets (Twitter has an auto-translate button!), here are links to the various members' Twitter accounts:
They also have Instagram accounts:
Some are on YouTube:
For general background information on the group, there's always Wikipedia (the Block B discography article has chart rankings and the like). Wikipedia also has an article on K-pop culture that can help outsiders understand what it is that Block B is constantly mocking.