The instruction sheets were part of Aldrin's own manual used while Armstrong piloted the Lunar Module Eagle towards the Moon in 1969.
Aldrin is selling the sheets after a change in the law last year paved the way for Apollo astronauts to retain legal ownership of items they kept from their missions.
The sheets are expected to fetch around 60,000 pounds when they are sold by Bonhams auctioneers in New York on March 25.
It reveals that the first words spoken on the surface were "Contact Light", by Aldrin to confirm touch down, The Telegraph reported.
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A letter by Aldrin which accompanies the sheets describes the moment an alarm sounded when the astronauts were close to landing on the Moon.
"The lunar landing was an experience I will always remember...Some eight minutes into our descent engine burn, we started our most challenging part of the landing - the approach phase sequence," the letter states.
"Neil's flying tasks suddenly became more complicated because the computer was sending us into a large crater containing and surrounded by boulders.
"At about 500 feet above the lunar surface, Neil Armstrong entered the commands to manually fly Eagle to the lunar surface with computer support.
"He slowed the descent rate to just a few feet per second and studied the surrounding terrain.
"Neil asked me about our fuel status and I indicated we had eight per cent remaining. I was then able to glance outside and began to understand why the landing sequence was taking longer than planned - the craters, rocks and boulders seemed to be everywhere.
"Neil was almost to the surface when a haze of dust was kicked up by engine exhaust. He could not see the surface and had to locate something just above the dust cloud.
"Finally Neil was able to see a rock that appeared fixed in the stream of dust. This gave him a surface reference.
"Just as Neil placed Eagle gently on the lunar surface, I spoke the first words from the Moon: 'CONTACT LIGHT!' This was the indicator light on our control panel that told us that Eagle had touched the lunar surface.