You don't need to open an account with ANZ to access Direct Broking in order to buy and sell shares, any bank of your choice will do.
Direct Broking allow Kiwi investors to trade NZ and AUS shares using their Cash Management Trust Account or through telephone, however more costly than trading online.
Payment will be made to your CMT account either for NZX or ASX transactions on the specified date in the Contract Note provided to you. You should have a CMT account upon registering with Direct Broking Online.