You must be a group member to post content to a Group.
Admins decide what type content appears. In many groups, anything by a Group Memmber will appear someplace. For examplee their might be a box for Member's Blogs, or Member's articles, etc.
However, there is also content that is specific to a group - meant to be on the topic of the group, not just by a group member. If a group member uploads content - a video, audio, article, or blog - he or she can tag it not only with a topic or place tag, but also with a group tag. Admins can then opt to, and typically will opt to, display content that is tagged for the group.
You can see both these type boxes on many group pages....so when you have content that is specifically for a group, tag it as such.
Finally, if you have ideas for content to display in a content box - text or links or graphics, say - or to display using the left menu - and so on - you can write an email to the admin making the suggestion, even including the materials, etc.