In the movie how do first-years know which House they'll be in?

The house elves fixed the robes after they were placed in their houses.They have all black robes on and later in the movie they have robes for each house.(In the book the house elves did it. It is not explained in the movie though.)

they don't. If you look closely, before the sorting they have black ties instead of House ties. I'm guessing it changes magically after the sorting.

The sorting hat tells them which house to go to. They probarly get their robes by magic.

The way they find out which house they are in, is through the sorting hat. The sorting hat is placed apon the child's head and the sorting hat looks into their mind to find which house would be the best for them to get the best they can out of Hogwarts.