2 ways to setup the subwoofer.
1. Use your soundcard outputs (if it is multichannel). Plug speakers to front channel output. Plug subwoofer to Centre/LFE channel (or plug into rear channel out if your soundcard doesnt have a subwoofer out). Use your soundcard software to configure the crossover.
2. Let the subwoofer manage your speakers. Plug the subwoofer into your soundcard (front channel out). Then connect your speakers to your subwoofer. Adjust the crossover on your subwoofer and speakers so they match (commonly at 80Hz).
With regards to your picture, well I'm not really enjoying that one. There are 2 connections to the left speaker both requiring a standard banana plug (by the looks of it) or raw wire. Unless your left speaker accepts a stereo input, I'm failing to see the logic in that. Usually one cable from your subwoofer connects to your left channel, and another cable connects to the right channel lol.
You will need to find a cable that connects those banana plug terminals > RCA. This type of cable is rare, you might need to visit your local audio store or check online for one. This may be an indicator of the different power output of the subwoofer compared to the speaker. So if you do choose to use such a setup, turn the volume down completely, turn on the system. Then turn up the volume as required.
What is your total budget for speaker + subwoofer? and will you be using these in a lounge setup? or just sitting in front of your computer (as stated in your previous post)? You may be better off with a entry-level studio monitor 2.1 setup.