How would you act the part of someone who is described as aloof?

That depends on why they are aloof. Aloof means cool and distant.

Often this is because the person who is aloof is dismissive or disdainful of the person or situation they have in front of them so you should act snooty and above it all.

Sometimes people are aloof because they are uninterested in the person or situation they have in front of them so you should act bored.

Sometimes people are aloof because they are have something to hide so you should act mysterious.

Of the three, the first is the most likely.