How to connect my decoder to my home theater sound system?

Without knowing the makes and models of the gear in question, this cannot be answered.

A lot depends on what type of output your Dstv decoder has and what type of inputs your home theater has...about the easiest way would be to run an optical cable from the decoder optical out to the home theater optical in....Using HDMI cables is another good way to do it....

Any idea how vague this is!

Right your HTS will need an Input of some description.
If it has no inputs but is just a self contained unit then you won't be able to do this.
If it has a HDMI/ARC input then you'd need to connect that to a HDMI/ARC output on the TV, and connect your decoder to any other HDMI port on the TV. Then when you watch the decoder on the TV it will send the audio to the HTS which you just need to set to it's HDMI/ARC input (on the HTS).

Depending on the equipment there's literally a ton of other possible ways you may need to do this, but this should cover the most likely scenario!

AV recievers have their own full set of decoders, so I doubt anything added by some automotive gizmo, or whatever it is you have, will add anything except confusion. My suggestion is to read the instructions that came with your whatever it is. by the way, HTiBs dont connect to much of anything but the television. Its why people don't buy them..Aside from the likely optical connections it might or might not have, your HTIB, If that is what your "theater surround" system is, probably only has a set of stereo analog inputs/outputs on it,and maybe an extra composite video connection. On an AV receiver there might be a tape loop or additional vid /aud second source connector set on the receiver. otherwise you should consider a switching box to split the input line sources.