Help wiring "smart" light switch in existing space
It appears that your wiring is in conduit so the metal box will be grounded so a green ground wire wasn't needed. You can run a ground wire from the box with a 10-32 screw into the ground hole in the back of the box to the two switches or if the switches have a metal yoke, just screw them into the box.
The red wire going to each of your existing switches is your hot wire. The orange and yellow wires are your load wires for your fixtures. Your instructions for the new switches will tell you what goes where. If your switches require a neutral, that would be the two white wires connected together with the wire nut.