THAN is used when making a comparison:
Now that Lennie has an iPad, he spends more time on it than on his computer.
Robin’s younger sister is taller than Robin.
This summer the East Coast was hotter than cities in the Sunbelt.
THEN is used when one thing results from or follows another or refers to a particular point in time:
Sandra filed her report and then danced down the hall.
Bob announced he was on a diet and then finished all the doughnuts in the box (to get rid of them, he said).
If you lived during the 1950s in America, you then knew the fear of nuclear war.