Scroll over the "Posts" tab and select the Post Type for which you want to add the label filter.  Click on the the pencil to edit the Post Type.  Scroll down to the Affiliated Content section. Now you can select the Label Type and specific Label you want to filter by.

The first box allows you to select which label types the user can filter by.  Selecting a label type will add a filter bar to the post list on your site, with a dropdown of all the active labels under that label type.  Selecting multiple label types will display multiple filter bars, which can be used in conjunction with each other.

The subsequent boxes allow you to pre-emptively filter the post browser (list), limiting posts to those that are affiliated with the selected labels only.  Note that this is exclusive, meaning that if you pick more than one label, it will display only posts affiliated with all of the labels you selected.  For example, let's say you choose to filter the post browser by labels "Blue" and "Green."  That post list will then display posts that are affiliated with both "Blue" and "Green" labels, but not posts that are only affiliated with the "Blue" or  the "Green" label.

Submit the form, and your post browser will now be filtering by the options you selected.