The sad death of Neil Armstrong reminds us that after 12 Americans walked on the moon no-one else did. They were able to do it very quickly because they broke it down into stages – Earth orbit, lunar orbit, lunar descent, lunar ascent, home. Werner von Braun wanted a direct flight but was over-ruled and graciously accepted the change, making it all possible with his Saturn V rocket. Not a single one failed, and the first manned flight of it went round the moon.
Mars is more difficult technically because it involves a greater distance and longer journey times. Here's how it might be done much sooner than people are now predicting.
1. Send the unmanned ascent stage to land on Mars.
2. When we know it has arrived safe with all systems working, send the return vehicle (complete with supplies for the voyage) to Mars orbit.
3. When we know that it has arrived safe with all systems working, send the astronauts. They could fly direct to the planet, using a short route, or dock in Mars orbit with a waiting descent stage. From Mars orbit they descend, do their research, and use the waiting ascent stage to reach the return craft waiting in orbit.
What Apollo did not do that we now can do is to send some of the hardware ahead. This means we do not have to carry the entire mission hardware with us, and can therefore use smaller vehicles and faster, less time-consuming trajectories.
I cordially invite some of our techno-geek readers to suggest ways in which this might actually be done…[The historically minded might note that Neil Armstrong put the first footprint on the moon 8 years after President Kennedy's famous challenge. It was only 66 years after the Wright brothers' aircraft first flew]