it all depends on what currency is the money order. if it is in USD, then sign at the back (endorse the cheque) and then deposit the cheque into your account. if you have a USD account, then charges mostly is based on the amount of cheque, say 1/4% or at the min charges of $50 or $100. all depends on which bank you are using.
if it is in HKD, then just deposit the cheque like regular HKD cheque. if issue bank is not HK orgin, then your bank of course will charges you.
most likely your customer means to send the money order to you, so you deposit the cheque to your account, but if your customer is willing to wire the money order via bank, then you give details of your bank (Name, address, account number, account name), in this way, you will can collect $ quicker.
it all depends on your agreement with your customer.