You'll have to contact Support to find out if they got your payment. Or was this a monthly payment? If it was a monthly payment, I suggest you go with yearly, or two-yearly payments to save you the hassle of sending in money orders every month.
If your account did get set up and is active, I doubt they'll send you a bill. Check your Billing section in the control panel for expirations and any possible instructions for renewal. I use credit card, and Manage Account shows me my renew date and that I'll be automatically rebilled. If you go to the Make Payment section, it'll tell you how to send in a money order to renew.