@vishae I am not an expert and haven’t done it before, but here are some thoughts on a theoretical basis:

You should set the old domain to issue HTTP 301 Moved Permanently responses for every resource, pointing to its corresponding location at the new domain, so that any search engine results, etc. get updated before the old domain goes away.

You might also want to look at the referrer (I think it gets set to the old site on a 301) of visitors to the new site and then show a notice for a while to anyone who arrives from the old site, reminding them to update their bookmarks.

And then post a couple more times between now and the discontinuation of the old domain, reminding everyone of the upcoming change and to update their bookmarks, RSS subscriptions, email address books(?), etc. (I wonder if RSS readers update subscribed feed URLs automatically when they get a 301?)