If you are asking about purchasing a membership from Disney, you will need to make a downpayment (if you are financing) and then payments will begin after the contract has closed. If you are buying a resale, you will usually make a deposit with your offer to buy and then pay the balance prior to closing.
If you are talking about renting a reservation from a member, all terms of the transaction will be decided between the two of you. Many members will ask for a deposit (25-50%) when the reservation is made and you get the confirmation letter and then the balance would be due 30-60 days before arrival. In some cases, depending on the nature of the reservation, full payment might be demanded before even making the reservation (this would usually be the case with a reservation within 30 days, since the member is penalized if they later cancel.)
All rental transactions are negotiable between those involved, so make sure you are satisfied with any terms of the agreement. You might want to read the FAQ on the Rent/Trade Board for more information.