If you PC has an orange audio jack that is for the subwoofer (and center channel). If you don't have a subout you can split the green audio output and connect both the sub and the amp to that output.
You will need some kind of amplifier to drive the passive speakers. There are many options. You can get a circuit board amp that will need a power supply, a small digital amp, any power amp, integrated amp, or receiver (new or used).
I recently got one of these https/www.amazon.com/gp/product/B073VFK911/ref=ppx_yo_dt_b_asin_title_o03__o00_s01?ie=UTF8&psc=1
to drive a pair of similar speakers. Works fine.