Although the cover date is August, the indicia shows September, 1962
Although we are reminded to get the next issue of Amazing Fantasy to follow Spider-Man's adventures, this was the final issue. Spider-Man wouldn't appear again until March 1963, in Amazing Spider-Man #1.
Synopsis: The Origin story we all know and love. When mild mannered bookworm teen Peter Parker is bitten by a radioactive spider he gains the proportionate speed and strength of a spider, and the ability to cling to walls. He learns the hard way that with great power comes great responsibility.
Peter Parker is a High School nerd who lives with his elderly Aunt and Uncle. He is teased at school by kids like Flash Thompson, and has a crush on Liz Allen. During a field trip he is bitten by a radioactive spider and gains super powers. He becomes a wrestler for the money under the name Spider-Man. When he ignores an escaping criminal he thinks nothing more of it until that same criminal kills his Uncle Ben. He hunts down the burglar and turns him over to the police and decides to help others with his new powers.
Synopsis: A man is frantically speaking on the telephone to his wife about a news broadcast claiming there are Martians loose in the city. He tells her that the police are searching the city and that she needs to come home immediately. The last panel shows him wiping sweat off his face using his third arm while his other two are waving wildly in the air in desperation as he warns her that they might be discovered and arrested.
Notes: This story has the classic portrayal of 1950's and 1960's aliens, in this case Martians, that look just like us except for extra arms or eyes.