After joining a group you will have a 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.)
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 current group 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 on the correct group page. Whichever method you choose, both are acceptable.