See your other question about Open Arms.

New Dawn - assuming that it is the climbing, repeat flowering New Dawn and not the single flowering rambler Dr Van Fleet....
Prune after flowering to late winter. Cut out any dead wood as close to the main stem as possible. Prune side shoots to about half their length. I used to use Mother's Day as my guide for the latest weekend to prune my roses (don't have them in this garden, yet). If it's a big plant without good support then it might be worth cutting it back a bit before winter so that it doesn't suffer in high winds.

If you're new to roses it might be worth taking a look at the RHS pruning guides or getting hold of the Dr Hessayon roses book.