About the expression "hit the bottom"
The expression mentioned above is used when someone is used when someone is have a tough time
Is that right?

What I wonder is that is this used in spoken english or not?
Is this a old fashioned english? or written English?

I dont know when and how to use it(hit the (rock) bottom) appropriately

And could you tell me other way of saying "having a really tough time?"
Slang is ok

Question

About the expression "hit the bottom"
The expression mentioned above is used when someone is used when someone is have a tough time
 Is that right?
 
What I wonder is that is this used in spoken english or not?
Is this a old fashioned english? or written English?

I dont know when and how to use it(hit the (rock) bottom) appropriately

And could you tell me other way of saying "having a really tough time?"
Slang is ok

Answer

"hit rock bottom" is the common usage (not: "hit the bottom").

"rock bottom" means the person is having a hard time, but it also means that it is the *worst* point for that person. If someone has hit "rock bottom" it means it can get no worse for that person.

This is a commonly understood term, used in spoken and casual written English. It is not old English, and it is not used in formal writing.

@AnthonyNewJersey's examples are good!

Answer

Here are a few examples Eric:

I saw Jane last night, she looks good, but after her divorce she looked like she hit rock bottom.

Jimmy was arrested again for drunk driving. I thought he hit rock bottom for the first offense, but he will never learn.