On the top-left of your picture near "MET", there is a set of icons, they display the comm status of your ship. These are important when you want to transmit science or control automated probes. You can hover on them with the mouse to have more information, here :
- ship is "kerbal capable", anyone can put a manoever node (a pilot is on board or you are playing science or sandbox mode)
- 0% signal strength
- no science data can be transmitted
- no connection to Kerbin
You must be on the hidden side of Mun, therefore you cannot transmit science since you don't have a line of sight with Kerbin.
Antennae orientation is not important for transmission or control, they just need to be deployed.
Near Mun and Minmus, any antenna (except for those embedded in command pods and probes) is sufficient. For example the Communitron 16 (radial, to avoid forgetting to deploy it) and the HG-5 are OK and cheap. You can see the range of the other antennae here.
As you did in your answer, either put a ship nearby with a relay antenna or land on the other side. You can also bring back the science to Kerbin to have additional points!
Here are other examples of display:

- probe capable ship (manoever nodes, precise throttle,...)
- very high signal
- transmissible science (data goes out of ship)
- direct connection to Kerbin

- probe capable ship
- very low signal
- relayed signal (via xenosatjool)
- transmissible science
- direct connection to Kerbin
- (map view only) signal jump filter to show how is transmitted the signal