First, make sure you have followed the steps above to associate the label and label type to the Posts application and to your post type.

In the top menu, navigate to "Posts" -> [Your Post Type].  If you have not yet added your post, in the right hand menu click on "Add new [Your Post Type]."  If your post already exists, navigate to your post and click on the gear to edit the properties.

Go to "Affiliated Content".  Find the label type that your label is under.  If your label isn't displayed, try clicking on the name of the label type to display the labels in that type.  Check the checkbox next to the name of the label you wish to affiliate with the post.  Feel free to check as many as you wish, but keep in mind that affiliating your post with many labels might make it harder for your users to navigate to the content they're looking for.

Submit the form, and your post will then be affiliated with that label or labels.