The descent stages of the lunar modules that put them there remain on the Moon. They are far too small to be seen from Earth, but you can spot the regions where they are with a small telescope. They all lie on the side of the Moon that permanently faces Earth.
Use the accompanying NASA graphic which marks the location of the landing sites of the lunar modules of Apollo 11 and 12, plus 14 through to 17. (Apollo 13 suffered an in-flight emergency that made its scheduled landing impossible).
Though all the sites are visible in the NASA artwork, which shows the Moon in a gibbous phase, you will have to pick your nights to see them for yourself. There will be some days when the Moon shows as a crescent in the sky, for example, leaving some of the landing zones in darkness.
You can check what phase the Moon is at by visiting our monthly guide to the night sky.
Incidentally, though the Apollo hardware left on the Moon is too small to be seen from Earth, much of it has been photographed from lunar orbit by robotic spacecraft.
Apollo 11: The first, historic landing of humans on the Moon, by the lunar module Eagle on July 20, 1969, was on the relatively smooth lava plains in the southern part of Mare Tranquillitatis, the Sea of Tranquility. This sea can easily be seen as a grey blob, using binoculars or even with the unaided eye.
Subsequent missions were more ambitious and went to more geologically complex parts of the Moon.
Apollo 12: Lunar module Intrepid touched down in the southeastern region of Oceanus Procellarum, the Sea of Storms, on November 19, 1969. The most western of the landing sites, it only comes into view towards the end of the second week after new moon.
Apollo 14: The crew visited a place called Fra Mauro in the lunar module, Antares, landing on February 5, 1971. Their landing site is a rugged area of highlands, named after the Fra Mauro crater that lies within it. Relatively close to Intrepid’s landing site, it also only comes into view in the second week after new moon.
Apollo 15: Lunar module Falcon came to land in the Hadley-Apennine region, on the mountainous, eastern edge of Mare Imbrium, the Sea of Rains, on August 7, 1971. They were able to explore a winding channel, or canyon, known as the Hadley Rille. This can be seen with larger amateur telescopes when the Sun is shining onto the Moon at the right angle, producing shadows. Try around the end of the first week or third week after new moon.
Apollo 16: Another mission to a more rugged region of the Moon. Lunar module Orion touched down on April 21, 1972, in the Descartes Highlands, named after a prominent local crater. It lies to the west of Mare Nectaris, the Sea of Nectar, which shows in a small telescope or binoculars as a dark grey patch on the Moon. The site comes into view from towards the end of the first week after new moon.
Apollo 17: The last of the Apollo missions landed its lunar module, Challenger, in the Taurus-Littrow valley on December 11, 1972. You can find this site on the southeastern edge of Mare Serenitatis, the Sea of Serenity, along a ring of mountains formed by a huge impact by another object in the Solar System. The landing zone is the first to come into view during the lunar month, becoming illuminated by sunlight while the Moon is a fat young crescent.
Related: Guide to the Moon