1
I like to search information on the internet.
I like to search for information on the internet.
I like to search the internet for information.
I’ve been searching my ID card all morning.
I’ve been searching for my ID card all morning.
Use search for + person/thing when the person or thing is what you are trying to find: ‘I searched for my keys all morning.’ ‘The police are searching for the missing child.’
Use search + person/place + for + thing when you examine a person or place carefully: ‘The police searched the car for drugs.’ ‘She searched her bag for her phone.’
2
We are searching for a house where we can spend the summer.
We are looking for a house where we can spend the summer.
Look for is more common in ordinary everyday situations. Search for is also correct, but it often suggests a more careful or organised effort and can sound more formal.