The system is built to include as many automated functionalities as possible. Members are sent an email under which they can verify their listing and once they do so their listing will be live in searchable.

If you would like to manually approve members before they are searchable on your website, I would suggest that you make the signup membership level a hidden and non-searchable membership level. Once you have approved their listing you can manually switch them over to a searchable membership level.

Go to the Search Visibility tab:

Please refer to the instructional article below to learn how to manually switch members membership level in the admin section. 

How To Manually Change A Member's Membership Level (Manually Upgrade Or Downgrade Members)