Get a cardboard carton (the ordinary, brown, unprinted type) and put the apples in there, in layers that are separated by newspaper. Don't let the apples touch each other.
Chat up your local green grocer for the small wooden crates tomatoes come in. Lay the apples in those so they aren't touching and stack the crates in a cool dark place, a cellar would be ideal.
Apples are often delivered to supermarkets, etc. in boxes that have moulded cardboard 'trays' (they are a kind of purple colour) that keep the fruits apart. You might be able to cadge some of them from a shopkeeper.