How does the signal get to the sub?

Very well, thank you! In fact as you can see in the photo (by Greg Sharpe), with the proper housing for your radio transmitter and some scuba gear, you can even escort your model underwater. The radio signal penetrates fresh water as deep as most people are willing to take their boats. Many modelers report that they have stayed in control of their subs several hundred feet (horizontally) from where they were standing. When asked "How deep will the sub go?", Jeff Jones, lost foam method hull guru has been known to say "All the way to the bottom if I'm not careful!"
Heavy minerals in the water or chlorine content in a swimming pool will limit the signal depth, depending on signal strength and frequency. Salt water is pretty well impenetrable given typical the low power and relatively high frequency of radio control units. Crafty sub modelers such as Mike Dory of California and Martin Calleja of the Mediterranean island of Malta have figured out ways to run their boats in saltwater by allowing the radio receiver's antenna to protrude above the surface.
Heavy minerals in the water or chlorine content in a swimming pool will limit the signal depth, depending on signal strength and frequency. Salt water is pretty well impenetrable given typical the low power and relatively high frequency of radio control units. Crafty sub modelers such as Mike Dory of California and Martin Calleja of the Mediterranean island of Malta have figured out ways to run their boats in saltwater by allowing the radio receiver's antenna to protrude above the surface.