How does neil armstrong came back from moon?

The return began with the most delicate maneuver of the trip: igniting an engine with no backup. The Eagle's ascent stage separated from the descent stage and lifted off from the Moon at 17:54:01 UTC on July 21, 1969, after 21 hours and 36 minutes on the surface. Michael Collins was waiting above in the Columbia, and docking occurred at 21:34:00 UTC. Armstrong and Aldrin moved into the command module with the 21.55 kg of lunar rock and soil they had collected, leaving the now-useless lunar module behind.

What turned a flight around the Moon into a return trip was trans-Earth injection: at 04:54:42 UTC on July 22, the service module's main engine burned for two and a half minutes and pushed the spacecraft out of lunar orbit. It was a maneuver with no backup plan, since a failure there would have left the crew circling the Moon with no possible rescue. From that point on, the journey was essentially a fall into Earth's gravity well, with small course corrections and no braking maneuver: the atmosphere would take care of that.

On July 24, 1969, after a mission time of 195 hours, 18 minutes and 35 seconds, the Columbia splashed down in the Pacific at 16:50:35 UTC (12:50:35 p.m. EDT), at 13°19'N and 169°09'W, 13 miles from the aircraft carrier USS Hornet, which recovered the three crew members. The recovery capped off a procedure rehearsed down to the last detail: the reentry profile had to shed the speed of the return trip without straying outside the thermal corridor, a narrow path between bouncing back into space and coming in too steep. The heat shield and parachutes were the last systems the crew depended on; the only way home was to turn that energy into heat and let the ocean do the rest.