Learn Swedish: Killen bor i staden. - The guy lives in the city.

The word en kille is a very common, everyday word for a guy or a young man. While pojken means the boy (usually a child) and mannen means the man, killen is used almost exactly like "the guy" in English. The -n at the end makes it the definite form (the guy).

Why does the verb bor end in -r instead of -ar or -er?

The dictionary form of the verb is att bo (to live). Because the verb already ends in a vowel, you simply add an -r to make the present tense bor. Regular verbs that end in a consonant take -ar or -er.

How is staden formed from the dictionary word for "city"?

The Swedish word for "a city" is en stad. Because it is an en-word, you attach -en to the end to say "the city", making it staden.

I sometimes hear Swedes say stan instead of staden. Which one is right?

They mean the exact same thing! Stan is just the shortened, everyday spoken version of staden. You will often hear Swedes say i stan (in town), but staden is the standard written version.