How do I transfer domain and website with the least amount of downtime?

It is better NOT to notify your current hosting provider. Here are the steps:

1. You need a hosting account with SINGHOST.NET. You can order a hosting account here: http://singhost.net/hosting/web-hosting.html
2. After you order and make payment, you will receive an account setup email after an hour or two.
3. With our hosting account information, you can upload your website and create email addresses.
4. It's time to go ahead and request a domain transfer with your domain registrar. Point the domain name to our name servers (find it in the welcome email) and wait until the changes have propagated.
5. About 24 to 48 hours after your domain registrar make the transfer, your domain should be pointing to your new hosting account with SINGHOST.NET and your website as well as emails should still be up and running without any problems.
6. Let a few days pass by just to make sure your domain points to your SINGHOST.NET hosting account everywhere in the world. You can now cancel your old hosting account with your old hosting company/email provider. To check: go to command prompt: type ping yourdomainname.com, if it returns your IP address (sent in welcome email), it would be correct.