Posts from groups that you are a member of, will appear in your main feed and of course posts in the group will be visible to followers of the group in their own feed.
If you want to see the posts from a group or add a post in one of the groups that you are a part of, tap on Groups at the top of your screen, tap on the group you want to post in and tap the Post button at the top of the screen.

You can post pictures or videos just like in the normal feed, but please note that you cannot post to multiple groups at the same time and if you want to make a post in the group and to your profile, you will have to make two separate posts, one to your profile and one in the group.