Commercial Crew astronaut Eric Boe practices docking operations for Boeing's CST-100 Starliner using a part-task trainer designed to mimic the controls and behavior of the spacecraft. (NASA/Dmitri Gerondidakis)

ST. LOUIS—It starts here in a warehouse by the airport. A couple of NASA astronauts in their blue flight suits, sitting at a touch screen display, taking the first training steps toward the real flights scheduled to happen more than a year from now.

Those flights will be the first from American soil since the space shuttle retired in 2011, another major milestone for NASA, which has been paying Russia hundreds of millions of dollars to fly U.S. astronauts to the International Space Station.

But now NASA’s best and brightest are learning to fly again. This time on new spacecraft, ones owned and operated by contractors, not NASA. Which is why astronauts Sunita Williams and Eric Boe were here at a Boeing facility Tuesday at the controls of a simulator, practicing a disembarking maneuver.

Williams and Boe—two of the four NASA astronauts chosen to fly in the so-called “commercial crew program”—are among NASA’s best, former military test pilots with previous experience in space. But Boeing’s CST-100 Starliner is a whole new spacecraft that they are learning to fly for the first time. So Tuesday’s training was rudimentary, designed to give them a sense of where the controls are, what the displays look like, the basic feel for the cockpit in what amounted to a sort of driver’s ed for space.

“It’s like learning to ride a bike with training wheels,” as Boe said. “This is where it starts. This is the first step.”

[Meet the first American astronauts headed to space from U.S. soil in years.]

In 2014, NASA awarded contracts to Boeing and SpaceX to fly astronauts to the International Space Station by 2017. It was part of a bold move designed to turn what’s known as low Earth orbit over to the commercial sector, which would allow NASA, with its limited budget, to focus on deep space exploration, such as getting to Mars.

First NASA awarded contracts to SpaceX and Orbital ATK to fly cargo and supplies to the station in unmanned missions. Now it is getting ready to put its astronauts on board Boeing and SpaceX’s spacecraft for the first human space flight to launch from U.S. soil in years.

With funding from NASA, and personal investments of a class of billionaires, including Elon Musk, Jeffrey P. Bezos, Richard Branson and Paul Allen, the commercial space industry has begun to take off. There is talk of companies soon flying tourists into space, reusable rockets that fly and then land again, even new space habitats that inflate once in orbit. (Bezos owns The Washington Post.)

“We used to talk about countries going into space,” Boe said. “Now we’re talking about companies going into space.”

Perhaps the most significant milestone will be the resumption of orbital flights from U.S. soil to the space station, some 240 miles high. Williams said she was looking forward to the day when tourists could pull up in their station wagons and watch the launches the way generations of Americans did through the Mercury, Gemini, Apollo and shuttle programs.

“This is the next chapter,” she said.

In addition to developing new spacecraft—SpaceX is making a passenger variant of its Dragon capsule—the companies are rehabbing launch sites at Cape Canaveral and the Kennedy Space Center in Florida. SpaceX plans to launch from pad 39A, where the Apollo lunar missions took off and many of the shuttle launched as well.

SpaceX’s Dragon and Boeing’s Starliner are different vehicles, with different feels and design, meaning that the astronauts, for now, will have to learn two different systems. The companies have the same goal—to fly astronauts to the station—but they are also in the middle of an intense competition over who will fly first. And so Boeing warned a small gathering of journalists watching the training session not to photograph the controls too closely, lest the competition see their design.

The astronauts said that while the spacecraft are different, flying is flying, and “physics is physics,” Boe said. “In the end it’s a spaceship.”

Both Boeing and SpaceX have built capsules, very different from the winged shuttle, that are designed to be largely autonomous. That, said Chris Ferguson, a former NASA astronaut who is now Boeing’s deputy program manager, is the future.

“The astronaut is really relegated to the role of a monitor,” he said. With computers flying, the astronaut is freed up to make sure all the systems are running smoothly, and can take over, if needed.

“If everything works right you’ll never have to raise your heartbeat,” he said.

Soon the simulators will be moved from the Boeing facility here to NASA’s Johnson Space Center in Houston, where the training will become more rigorous and intense, leading up to the first manned test flights, now scheduled to happen in late 2017.