Hello.
I would like to start off by saying I have no knowledge about car audio, or setting up a system in a car, but I have a 2x"pioneer ts-w309d4 champion series 12-inch dual 4-ohm 1400-watt" and I would like to know which amp I can use to power it.
Thank you for the help.

 

There are a varity of amps you can choose, whats your budget?

 

This particular sub has a 400W RMS power handling rating. And you have a pair of them, so ideally you'd want 800 to 900W available for the subs.
The 4ohm Dual Voice Coil configuration means that you'll likely wire the drivers down to a final load of 1 ohm, though you could wire for a 4 ohm load. The issue that may arise with 4 ohm load, is that the amplifier is going to have a be a big powerful unit to be able to produce 800W into 4 ohm, which will probably cost a lot more than an amp that can provide the same power at 1 ohm.
So you'll be looking for an amp that does 800 to 900W into 1 ohm (or 4ohm)...

Kenwood KAC-9105D Class D Amplifiers at Onlinecarstereo.com <<< 900W into 1 ohm & 2 ohm.

That would be a good match. I actually own the 8105 amp - its the baby brother to this one. I have been running an 8" sub for a couple months now, and haven't had any issues with the amplifier.

I'm not sure if these particular subs come in a 4ohm Single Voice Coil, or 2ohm Dual Voice Coil configuration, but if they do, either one of these would allow you to wire for a 2 ohm load. Finding an amp that does 800W into 2 ohm may be a lot easier than finding one that does the same into 1 ohm...

Infinity KAPPA ONE Class D Amplifiers at Onlinecarstereo.com <<< 800W into 2 ohm.

Rockford Fosgate R1200-1D Class D Amplifiers at Onlinecarstereo.com <<< 800W into 2 ohm.

Soundstream PX1.1300D Class D Amplifiers at Onlinecarstereo.com <<< 900W into 2 ohm.

You could find an amp, rather easily, that'll provide 1000W into 1 ohm. If you were to go that route, you'd have to be careful as you'd be 100W over the RMS for your subs.