You can only add a sticky post if you're a Group Owner or Admin.
Here's how to add a sticky post in a group:
1. While in the group click the "Add a Post" button at the top of the page.
2. After you create the title and the post, at the bottom you will see: "Post Status"
3. Select "Sticky" from the drop-down menu.
You can also sticky a post made by another member. Select "Sticky" from the drop-down menu. Under the members post.