You can't add a domain name until you've purchased the Web Developer account - this allows you to use up to 10 of your own domains. Free and Hacker accounts can't use custom domain names.
For now on your free account you can access your website via
manish.pythonanywhere.com - once you've got a Web Developer account, you will set up a CNAME at your domain provider which points to your PA hostname, so everything about your site will be the same except for the domain name to get to it. As long as your internal website URLs omit the hostname (which is generally good practice) then you can test everything about your site is working correctly before adding the domain.
Once your paid account is active, the only delay will be in waiting for your domain provider's DNS changes to take affect - this can typically take up to 24 hours, but is often quicker. This is not something that PA can do anything about, however. On the PA side with your paid account active you'll see the option to specify a domain name for your web apps on your dashboard.