What kind of soundcard do you have? How you wire it up depends on how those two TRS jacks on the soundcard are configured.
Basically, you’d want a 3.5mm to split mono cable like this running from the NTS-1 mini out to the two mono inserts on the soundcard. That gets audio from the NTS-1 back to the soundcard inserts - you’ll have to use two separate channels in the soundcard to control left and right from the NTS-1 since they’re mono, then mix them.
Assuming you want to send audio to the NTS-1 from the soundcard for processing and not just record the sounds straight off the Korg, you’ll also need one running from the soundcard output(s) to the mini stereo in on the NTS-1. The question is what kind of output the soundcard has. If it has dual mono outputs, you’ll need the same kind of cable as before. If it has a stereo output, you can use a mini stereo to 1/4" stereo cable like this to get audio from the soundcard into the Korg.