How to manage millions of users? I am about to launch something really big. I need to prepare my server and database.

I would like to group each set of 100,000 users in separate user tables but I do not know how to associate one user trying to log in to the appropriate user table.

For instance, how would I know that user jay@mail.com is related to the user table #36?

Would it be the same to have 10 millions users in one user table or 100 of 100,000?

How does Facebook? I can't believe they would have one global user table with 950 million entries.
You're not going to have a billion users tomorrow and MySQL can handle several million rows without any problem. I have 5 million users in my user table and trust me, it isn't even on my radar of things to worry about. 

Don't worry about sharding until you need to do it. You are attempting to optimize prematurely for a problem that may or may not ever exist and in the process, you will severely cripple the rate at which you can innovate. Be fast to launch and find the problems as they come. You cannot predict in advance what your scaling challenges will be.

When and if you ever reach this scale, you will then have quite a bit of money and resources to throw at this kind of problem.