The sticky post should be distinctly recognizable in some way in comparison to normal posts. You can style the .sticky class if you are using the post_class() function to generate your post classes, which is a best practice.
They should show at the very top of the blog index page, even though they could be several posts back chronologically.
They should still show up again in their chronologically correct postion in time, but without the sticky indicator.
If you have a plugin or widget that lists popular posts or comments, make sure that this sticky post is not always at the top of those lists unless it really is popular.