The inbuilt facility to do this disappeared with the demise of MobileMe. It is possible: some ISPs offer this facility (GoDaddy is one) so you should start by checking whether yours does.
If not, you can do it yourself provided your ISP allows you to add an .htaccess file to your foldere - not all do. Also it's not entirely straighforward if you are unfamiliar with the techniques involved.
This page describes the method:
Please note the caveats at the bottom of the page: this isn't a highly secure method and you should not rely on it to protect sensitive information.
The only other thing that you can do to create a private website is to re-create your website using WordPress which is a Content Management System (CMS) and if your host offers this, as many do, then it will be a one click installation running on your server and you can then make this a private website that require a username and password for people to enter.
If you use WordPress, then you also have other options. You can keep some of it private and can allow people to register on your website and you can assign them different access levels and WordPress then generates passwords for them.
Password protection is done on the server and how you do it will depend on the facilities offered by your host...
If you don't have a .htaccess file you can create one using Text Edit.app. Just don't add the dot until you have uploaded the file to the server or it will disappear!