Reward are based on your activities - the lowest reward goes to everyone, with better rewards going to the top 70% 40% 15% 5% Commanders respectively. Also apart from money reward to direct participants there are rewards to anyone - usually those are ship discounts. I have seen 30% Imperial Clipper discount.
You can find active community goals at every stations galnet news - all news with pencil icon are community goals.
To participate simply visit a station with an active Community Goal and open the Bulletin Board, the active Community Goals for that station will be at the top of the list.
Select the goal you want to participate in, read its description and click the "SIGN UP" button at the bottom.
You can now start contributing to the Community Goal. To check your current status open left user interface and check Transactions tab.
Visit active community goal thread to see current community goal locations and objectives.
There are 6 tiers in each community goal and more players contribute - higher tier can be reached and thus higher reward everyone will receive, but keep in mind that community goal will be closed when top (6th tier) will be reached.
Objectives range from bounty voucher and combat bond cashing, selling exploration data to delivering specific commodities.