Simple. All they had to do was:
- Pay Westinghouse and RCA a large sum of money to develop TV cameras small enough to fly aboard the spacecraft in an era when the typical studio camera weighed almost as much as a man and to operate within laughably tight power and bandwidth limitations. Westinghouse did this by using brand new technology, settling for a non-standard low frame rate and resolution, and taking certain technical shortcuts, some of which make the image quality less than what it might have been, but which contributed to the development of the home camcorder a few years later.
- Pay RCA a similarly large sum of money to develop transfer equipment capable of reading the non-standard signal (broadcast back to Earth as part of the spacecraft’s S-band data transmission, not on the TV band) and convert it to NTSC format for transmission to the networks. The conversion of one analog signal format to another using the technology of the time required the invention of a primitive forerunner of the DVR (which would lead to commercial instant replay a few years later) and the expedient of “filming” off a specially made high brightness TV screen using a standard studio camera.
- Pay a similarly large sum of money to set up or acquire transmission links back to Houston. Where today you’d just use the Internet and twenty years ago you’d lease a T1 line, NASA had to build the network from scratch.
- Pay many millions more to build or lease and equip the facilities of what is now called the Manned Spaceflight Network, using large parabolic dish antennas spaced around the world to provide continual coverage as the Earth turned and redundant coverage (which came in handy), with supplemental ARIA aircraft and ships to fill in gaps in coverage.
- Plan the entire mission months in advance so that, by launching from Florida within a certain window, they would arrive at key mission objectives with the sun in a suitable position to see landmarks and targets clearly and without having the sun in their eyes, and then preplanning TV shots to avoid shooting into the sun and destroying the camera (though that happened once anyway) or shooting under lighting conditions beyond the range of the primitive camera.
- Invent large, collapsible parabolic S-band antennas that could be carried by the Service module and LM, and that could be deployed on the lunar surface for improved signal strength.
- Plan time into the flight plan in which to test the TV equipment ahead of the landing. For example, during Apollo 11, about ten and a half hours after launch, right before the astronauts went to sleep, Houston asked them to shoot about ten minutes of basically anything just to exercise all the moving parts needed to get the signal back home and out to the networks.
- Design and test a camera mount that would allow a camera mounted outside in a storage locker to be easily and reliably deployed by the first astronaut to step outside and then televise his progress down the ladder.
- Design and test a pan/tilt head that would allow a camera mounted on a tripod (or later, a lunar rover) to be controlled remotely from Houston.
- Plan, test, practice, execute.
In short, by planning every detail and paying a lot of money. Transmitting a signal from the moon to the Earth is not hard, there’s nothing to get in the way except Earth’s atmosphere. S-Band was used because it could penetrate the atmosphere, but getting the signal broadcast around the world was much harder than getting it back from the moon—of course, there was already some infrastructure in place for that.