“He likes to act like he doesn't know anything about it.”

You're talking about a social networking site with your family. Your husband asks a question about it, but calls it by the wrong name. You think he did that on purpose. You say to your daughter:

He likes to act like he doesn't know anything about it.

(someone) likes to act like (clause)

Use this expression to talk about someone who "puts on an act". In other words, someone who pretends to be something that they're not. For example:

He likes to act like he knows everything.

She likes to act like she's so innocent, but you and I both know that's not the case.

You like to act all big and tough. Please! You're a total softie.

Talking about people this way sounds negative. In the example above, the wife might be annoyed that her husband pretends not to know about the social network.

(someone) doesn't know anything about (something)

For topics that you completely don't know about, you can say "I don't know anything about ___": 

A: Do you know how to burn a DVD?

B: No, I don't know anything about that kind of stuff.