When you say you have a new subwoofer do you mean a raw driver? If so, you'd need to know the impedance of each voice coil on the driver and what the impedance of the amp is. Then you can either wire the voice coils in series or in parallel based on your amp. Wiring in series will double the impedance value while wiring in parallel will reduce the value by half. So if your driver is a dual 4Ohm voice coil wiring in series will yield an 8Ohm load to the amp while wiring in parallel will present a 2Ohm load. You might also get better results if you posted in the DIY forum instead of here. This forum is more for completely built subwoofers.
On the other hand, if you are talking about a store bought passive subwoofer box with high level L/R speaker inputs and by "box" you are referring to is your receiver then you should be able to connect the subwoofer out from your "box" and connect it to either of the inputs on the subwoofer. Now if the L/R inputs you are referring to is a powered subwoofer with L/R RCA inputs and your "box" doesn't have a low level RCA output for the subwoofer channel then your only option would be to get a converter or new receiver with a low level RCSA output for the subwoofer.
Pictures or models of your two items would go a long way in helping us to help you.