Apollo 11, carrying Mission Commander Neil Armstrong and Lunar Module Commander Edwin "Buzz" Aldrin, landed on the Moon on the afternoon of Sunday, 20 July 1969. At that time, the Moon appeared in the southeastern to southern sky for viewers in North America. Several hours later at nightfall, it appeared in the southwestern sky for much of North America, about halfway between the planet Jupiter and the star Spica, and roughly 35% illuminated.
The simulated image here, courtesy of Starry Night software, shows the Moon in the southwestern sky, flanked by Jupiter and the bright star Spica, as viewed from Houston, TX at 9 p.m. CDT on July 20, 1969
The landing location is at the southwestern edge of Mare Tranquillitatis, just north of the lunar equator at coordinates 0.67408°North, 23.47297°East. When viewed on the Full Moon seen from Earth, the location is just to the right of the center of the lunar orb. From any clear location in North America, the Moon and the landing area were clearly visible at the time, although of course no earthly telescope was strong enough to actually reveal the events as they unfolded. (For all Apollo program landing locations, see here: http://is.gd/3Fq3eg)
At nearly 6 days old (that is, 6 days since "New" phase), it was in a Waxing Crescent phase, about to become First Quarter. The timing of the landing was chosen in large part to provide long shadows at the Apollo 11 landing site, making surface features easier for the astronauts to see as they negociated for a clear spot to touch down.
Roughly a quarter of a million miles from Earthbound observers, in the Lunar Excursion module (LEM), the landing indicator came on at 20:17:39 Universal Time (UT), or 39 seconds past 3:17 p.m. Central Daylight Time (CDT) on July 20. At the last moment, Commander Armstrong discovered that the spot that the computer had targeted as the landing point was too rocky. He took partial manual control, landing the craft in a safer location a short distance away. The lander had about 25 seconds of fuel left at touchdown.
Armstrong became the first human to step onto the Moon 6 and half hours later at 2:56:15 a.m., UT on the 21st, or 15 seconds past 9:56 pm, CDT. Aldrin first touched the lunar surface at 3:15:16 UT on the 21st, or 16 seconds past 10:15 p.m., CDT on the 20th.
After roughly 2 and a quarter hours on the lunar surface and with nearly 50 pounds of samples, the astronauts returned to the LEM, Aldrin first, closing the hatch on the lunar environment at 5:11:13 Universal Time on the 21st, or 13 seconds past 12:11 a.m., Central Standard Time on the 21st of July.
The LEM lifted off the lunar surface at roughly 12 hours later at 17:54 UT on the 21st, or about 12:54 p.m. CDT. Rendezvous with the Command Module came at 21:35 UT, or 4:35 p.m. CDT. Engines fired to return to Earth at 04:55:42 UT on the 22nd or 42 seconds past 11:55 p.m. CDT on the 21st. The Command module touched down in the Pacific Ocean at 16:50:35 on July 24, or 35 seconds past 11:50 a.m., CDT, successfully completing the mission.
The full Apollo 11 timeline can be found here: http://is.gd/XoDIdj