Let’s look at the easier one first. The word than is used after a comparison, so it often accompanies comparatives like taller, better, and smarter (to name just a few) and words such as more, less, and fewer.
Tim is taller than Tom.
Sunset is later this month than last month.
Cassie has fewer paperbacks than her sister has.
Then is used when referring to time or a sequence of events.
We’ll see you then.
She walked to the corner and then crossed the street.
Come to the diner, then we can order breakfast.
Combined with the word if, then can also mean in that case, or as a consequence.
Example: If the car is in the shop, then I won’t be driving to work.
Remember, use than in comparisons and then for everything else. Knowing the difference between than and then means you’ll never find yourself in this situation, from Season 1 of The Wire.