With the directory you also need to export your PHP Scripts database(.sql file).
Create a Domain in Ampps with same name as your live site. Set the path as you wish. Don't forget to check in Advance Settings to add an entry to hosts file.
http://localhost/ampps/index.php?act=ampps_domainadd
Let Apache restart.
Paste the contents of your web directory into the path you specified.
Create the database in the localhost. Keep the name, user and the password same if possible. Else you will have to change your PHP Scripts config file accordingly. Don't forgot to give the user all privileges to the database.
Import the .sql file which you exported from live server to the database which you just created.
If your PHP script is using Absolute path anywhere like /home/user/anything then you will have to replace that path with your actual path of Windows/Mac in the whole script.
These steps should import your website to localhost.