I don't know what this line is even called: "-"
Anyways, what is the name of it, and under what circumstances should it be used in?
Also, I sometimes see it with two lines: "--", instead of one. When can each one be used?
I found an example which uses the "--" version:
They are the second American League team to draw 4 million fans -- the Blue Jays are the other -- and third in the Majors. Toronto and Colorado each surpassed the mark in 1993; the Blue Jays had done so in 1992 as well.
If it's joining two words, it's a hyphen. Some people use a longer one, called an en dash (becuase it is as wide as a letter 'n') to join things specially for that text, though nowadays most people use a hyphen there. When used as punctuation, it is called a dash, traditionally called an em dash because it was bigger (the width of a letter 'm'). So some people use two dashes to get this effect. In a word processor like Words, if you use two dashes, it will convert them into an em dash for you.