How to install remote switch for ceiling fan?
While the picture is not quite clear, it looks as if the red wire on the left is connected with a wire nut to two black wires. The red wire on the right appears to go elsewhere (probably to the fan).

If so, the left wire is hot. This  can be confirmed by carefully turning the power to the fan on. Using a non-contact tester, the left red wire should show power, and the right should not.

If that tests out, turn off the power, connect the left red to the switch wire with the yellow label. Connect the right red wire to the switch wire with the blue label. Cover each connection with a wire nut.

Connect the green switch wire to the bare copper or green wire(s) that should be deeper in the box (ground). If there is no ground wire, attach the green wire to the box itself using a screw or grounding clip.

Remount the switch. Turn the power back on. Check the switch.

This is a fairly simple connection. However, it sounds like you have very little experience working with electricity. Be very careful! Make sure all connections are tight, and no bare wire is exposed (other than the ground). It is often a good idea to watch someone with some experience before trying projects out on your own.