If you search for something or someone, you look carefully for them.

If you search a place, you look carefully for something or someone there.

A search is an attempt to find something or someone by looking for them carefully.

If a police officer or someone else in authority searches you, they look carefully to see whether you have something hidden on you.

If you search for information on a computer, you give the computer an instruction to find that information.

If you go in search of something or someone, you try to find them.

You say 'search me' when someone asks you a question and you want to emphasize that you do not know the answer.