basically, "to look *FOR* something" is the same as " to search for something".
(note: "to look AT something" is different.)
"looking (for)" is more commonly said than "searching".
search for = look for.
search something = look for something in something.
searching is usually more formal or serious, like searching through a book, or searching for gold.
looking for can be more casual, or when looking for people.
sometimes, "searching" is used when you have a very specific target, whereas "looking for" is done when you are not as serious about something, or you are not as sure
examples:
I am looking for Mr. Jones. ( i want to find him and talk to him )
I am searching for Mr. Jones (he got lost in the woods and it is getting dark outside )
I am searching through a telephone book for the right number
I am looking for the number in the telephone book.
(both work, but we usually say looking)
I am looking for someone who wants to have a good time.
I am searching the streets for anyone who wants to have a good time tonight. I am really desperate!
Yesterday I lost my keys, I was searching for them frantically !
I have to go in 2 hours, and I don't know where my keys are. I better start looking for them.
I'm looking for a job now. (We say this instead of I'm searching for a job, usually. Searching for a job could be said, but since you don't know what job you're going to get yet, you just want any job, you say looking for.).