"Like" can be a preposition that means "similar to." It's used before a noun or pronoun.
Examples: > I look like my mother. > He has dark hair like me. > He swims like a fish. > I work like a horse.
You can't use "as" in any of these sentences. "As" can also be used before a noun or pronoun, but not to talk about similarity. We use "as + noun/pronoun" to say what job or role a person or thing has. For example: "He works as a policeman." It's important to not mix up "as" and "like." If you say "I work as a horse" instead of "I work like a horse," it means that your job is to do what a horse does. :)
"As" can be used as a conjunction before a clause (with a subject and a verb). It means "in the same way that."
Examples: > I eat Korean food with metal chopsticks, as they do in Korea. > Nobody understands him as I do. > He want to Harvard, as his parents had before him.
You can use "like" instead of "as" in the sentences above. It would not change the meaning. The difference is that "as" is more formal than "like." Also, some people think that only "as" should be used before a clause, and "like" should be used only before a noun or pronoun not followed by a verb. My advice is to use "as" before a clause whenever you take an English exam or write an essay, but use whatever you like when speaking to your friends, etc. :)