What are the requirements for supporting millions of users on your website?

Supporting in what?
Can you maybe add some detail?

I mean would the site run different (slow, for example) if that many people were on it? Or is there a limit to the number of people that can access it without you making some sort of upgrade? Sorry to be so vague, but I don’t know anything about this subject.

Aha, thanks for clarifying.
I think you would need a big server (space), but that is (something I think I know) merely because I have seen discussions about that on Fluther (about Fluther migrating to a new (bigger) server).
I am sure that there are some tech Jellies that can answer you much better though.

Yes, it will slow down if huge numbers of users come to the site. Whatever the web host server is, it has some limits.

How much it slows down depends a LOT on what users do on your site, how much computing is required by the site to accommodate them and how much data are transferred from the users and back to the users.
...And how many users come to the site.
If you really expect millions then get a system architect involved and/or contract a server farm like Amazon has.
Presumably you have the site built, and whatever it is can probably be scaled by some skilled server architects.

What sort of site is it? Do the users write text? ...Work with pictures? ...Play games?

bandwidth bandwidth bandwidth
and server space

There are some small companies who have had their websites totally crash after a burst of unexpected media coverage so that no one could access their website until they upgraded to another tier of service or a different webhost .

As a matter of fact, I saw a documentary about this regarding the “Oprah Effect” where in the first few years, small entrepreneur were totally overwhelmed by a brief mention on her show. Subsequently, especially prior to her “Favorite Things” show each holiday season, producers from the show work with these small business owners months in advance to prevent a catastrophe.

Obviously, the first order of business is making certain that they have the web service structure in place to handle the enormous traffic load.

But for most small businesses and websites, the increase in traffic happens more gradually and the owners have time to adjust their hosting plans.