The easiest way to create content, and automatically link it to the group where it belongs, is to be on a Group's home page that you have subscribed to, (e.g., this page).
When you Subscribe to group you will find the Group dashboard, in the left sidebar, at the top of the group's home page. (If you cannot find the dashboard you have not joined the group.)
The Group dashboard makes it easy to create the content types available. Simply clicking the correct button, automatically leads to the correct Create form linking your content to the group it belongs via the Groups audience field.
To post to additional groups you have joined, go to the bottom of the Create form, and in the Groups audience field, you will find the group name you are viewing already placed there automatically. Add any additional group(s) you wish, separating each with a comma.
Adding and linking content, when not on a group page is almost as easy. It just takes one additional step of manually linking to the correct Group in the Groups audience field. As already mentioned, this is done automatically if you start in a group you have joined. Either way, both methods are acceptable.