You've probably also noticed an airbag (SRS) light on your dash? Neither the airbag nor the horn will be functional like this.
The three small socket head screws around the center hole of the wheel hold the slipring in place- this is the plastic cylinder that contains the electrical contacts for the airbag and the horn. The slipring on the wheel now looks kinda fuxd up somehow.
Part 3 here-
Link here. Notice the wires? They are there to hook up the airbag and horn. It looks like you can put a slipring on that wheel with no problem, and it should work then with the horn and airbag. Sliprings are wear items- it's very common for them to require replacement (when the horn stops working or that SRS light on your dash comes on). Do a search for the part number. You may be able to pick up a used one on Ebay or the like, or get a new one.