3. Update Your DNS Records (Domain Name Holders Only)
If you have your own domain name, and you're shifting it with your website, update your DNS records with your registrar only when you're satisfied that your new site works as intended.
If you have a new domain name (and you did not have one previously), simply point the domain name to the new host. Do NOT point the domain to your old host first for fun. This will cause additional complications as well as delays in your domain name propagation. Propagation seems to be faster when you're pointing a brand new domain than when you're switching a domain between IP addresses.
Although the registrars tell you that the update should be completed within 48 hours or so, in practice it actually takes about a week for all the name servers around the world to catch up with the new location of your domain. In that interim, only some parts of the world will be able access your domain at your new host; the rest will continue to access the old site. Note that even if you see the new site in your browser, it is not necessarily true that others will see the new site. This is normal - do not worry.
i. Do not delete the old site during this interim. This will help you avoid losing visitors. Just maintain two copies of your site. Endure the inconvenience for this period - it's only a short term hassle.
ii. At this point in time, do not put up a page on your old site redirecting people to your new domain. It may seem like a good idea, but it isn't. It was one of the silly things I did in one of my moves and I really regretted it.
Why? While you may be able to follow your redirection page to your new host, it merely means that your ISP has updated their name servers so that your domain points to the new host. People who use ISPs elsewhere in the world may not be in the same situation. Some ISPs are very slow to update their name servers. When your visitors using those ISPs click on your redirection, they'll be redirected back to your old site again (since the domain is still pointing there for them). It'll be like an infinite loop - they'll keep going back to the same page redirecting them elsewhere.
I learned about this because I accessed the Internet using different ISPs. I was able to reach my new host with one ISP, but was trapped in an infinite loop with the other.
In general, if you're moving domains, you will not need to put a redirection page. Period