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 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.