Find

"Find" usually refers to the search for or the location of something lost.

Husband: I can't find my keys. I don't know where I left them. I think I've lost them.

Wife: Are you looking for these?

Husband: Where did you find them?

Wife: You left them in the your pants pocket.

"Find" also means to discover.

This morning I found a twenty dollar bill on the ground.

"Find" also means to experience in a certain way.

I found it quite strange that there weren't any people in the park.

"Find out" is to discover or resolve.

It took the technicians all morning to find out what was wrong with the machine.

Related Article: Figure out

Meet

We use "meet" to refer to the first time that we are introduced to a person.

Where did you meet your wife?

Woman: I'd like to introduce you to my boss. I'd like you to meet my boss.

Man: Hi, pleased to meet you.

We use "meet" to refer to a reunion of people.

Where shall we meet? Let's meet in front of the entrance.'

Bob: Do you know my wife? Have you met my wife?

Steve: Yes, nice to see you again, Jane.

Once you've met a person then you know the person but it's not uncommon to use meet when encountering a person on subsequent occasions.

It's nice to meet you again.