How do I add a directory to our website and control who and what can be seen?

Go to Settings >  Accessibility, then scroll down to Customize Directory/Member Access.

Customize what people attributes are visible in the online directory by checking the boxes for the attributes that you want to show.  You can also customize which Church Member Type is included in the directory by clicking the Church Member Types link. If someone doesn't want to be in the directory, 1) add a Church Member Type indicating that and do not include that type or 2) indicate "Yes" in the Unlisted people attribute field on that person's profile. Any Unlisted members will not appear in your online directory.

Copy/paste the directory link found in the highlighted green box just below the customization settings, but be sure to give the member password to anyone wishing to view the online directory.

Finally, the BEST way to access a directory is by having people text "me" to your Text-to-Church number and they can easily access it there without needing a link.