Each device provides relative installation instructions. The Capture card may be installed directly onto your PC motherboard or connected to your computer using a USB cable. The Capture Device will be connected from your console to your PC and TV/Monitor via HDMI cables.
Note: Older capture devices may have slight audio delays, so check the details on the capture device you have purchased. Capture devices installed directly to you motherboard via PCIe do not typically have any audio delay.
Once connected you can then use Streamlabs OBS or a similar streaming software to add a source for your video capture device and configure the rest of your stream with overlays and widgets.
Keep in mind that you may also need some additional equipment such as a USB microphone or audio mixer.