Example 1
Colton attributes his success with the ladies to both his winning personality and his enormous bank account.
In this shallow example, the correlative conjunctions both and and join forces to explain why Colton always has a date on Saturday night. Notice that "winning personality" and "enormous bank account" are both noun phrases; since they match up, you can use the correlative conjunction.
Example 2
Either Aisha threw a wild party while we were out of town, or our house was hit by a tornado.
Aisha is busted. The correlative conjunctions either and or are used here to link the two possible causes of why her parents' house is a disaster, and one of them is much more plausible than the other. "Aisha threw a wild party" and "our house was hit by a tornado" match grammatically, so either/or works perfectly.
Example 3
I'd rather jam pretzel rods in my ears than listen to Nickelback.
In this sentence, rather and than are a pair of correlative conjunctions that relate listening to Canadian rockers Nickelback to the pain of shoving salt-studded snack food in one's ear holes. Since "jam pretzel rods" and "listen to Nickelback" are grammatically equal, rather/than is a-okay.