Community goals are currently disabled and it is uncertain if they will return.
I find the best place to keep track of community events is the developer's forum. Here's the current thread:
https://forums.frontier.co.uk/showthread.php?t=187372
These threads tend to be highly detailed and viewing later comments may help in completing the requirements.
From bmlortz:
You can also find community events by checking the in-game Galnet News Feed. These in-game news stories will also contain buttons to highlight the galaxy map location.
When you arrive in the community event system, you'll need to check the bulletin board in the correct station. At the top of the list should be a mission that looks substantially different from the others. Make sure to select the "Sign Up" option when viewing it.
Just because you've signed up doesn't mean you'll get credit. You must also add at least some progress to the group goal. At the time of writing this for instance, there are 2 community events in the Kaushpoos system at Neville Horizons station, one is to collect bounties in the system and the other is to sell Palladium that you yourself mined. Word of Caution: These both, like all community events, must be turned in at the station were the event starts! (In this case, Neville Horizons, Kaushpoos)
Once you've turned in whatever the community event calls for at the correct station, you should be in. You can confirm this by checking the event in the transactions screen and making sure it says at minimum that you are in the top 100%. So long as the community has reached the minimum reward tier (if this doesn't happen, the event gets nullified for everyone), it's simply a waiting game for the event to end so you can claim your reward. The events end when either the final reward tier is reached, time runs out, or another community event that is tied to it ends. Return to the starting station to get your reward and achievement.
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If you wish to get some extra credits out of these, there are 2 ways in which community event value can increase, one personally and the other communally.
To increase your personal reward, repeat whatever the event calls for. When viewing the event details, you should see that it has multiple rewards based on what percentage of players you fall into on providing progress to the ultimate goal. As you increase your output to the event and move up the list, your reward also grows. You can lose reward levels if you get outpaced by other community members. It seems that most people will just meet the minimum requirement they can however, so losing levels should be a rare occurrence.
The community event also grows in value for ALL players, even those who got just a single point of progress in it, as the reward tier increases. The event progress is shown on the left hand side of the details by a bar graph with lines marking where the tiers are, the top of the graph marking the final tier and the early end of the event. This increases as more of whatever the event calls to is completed by the entire community as a whole.