Okay, there are two common lines when dealing with matchups (i.e. one against one).
The spread is a certain number of points that the favorite is favored by. If you bet on the favorite, you win the bet if it wins by more than that amount (“covers the spread”). A bet on the underdog pays off it it wins or loses by less than the spread (“beats the spread”). That’s what sports gamblers mean by “winning for real”; it’s the side that wins against the spread. If the favorite hits the spread exactly, it’s a push. Some lines include half points…6 1/2, 10 1/2, etc.; these are exactly the same except, of course, they cannot result in a push. How the sports book (that’s the place you bet on sports) makes money is via the “vigorish”, an extra amount you have to pay on losing bets. It’s not much…around 5% according to one source…but it’s enough to guarantee a profit as long as there’s nearly equal money on both sides. That’s the whole point of the line, to make both sides equally appealing.
In gambling paralance, “plus” refers to the underdog and “minus” refers to the favorite. Therefore, in your scenario, the Wildcats would be “minus fifteen”. Also, if you bet Duke, the nomenclature is that you “took Duke and fifteen points”, or simply “took Duke and the points”. (I’m unaware of any equivalent for the favorite.)
The plus/minus line (I’m not sure what this is called exactlY) places a 3-digit number in front of both teams, with a plus in front of the underdog’s and a minus in front of the favorites. E.g. Hawaii +900 BYU -780. For the plus side, this means that for every bet you make of that many cents, you get 1,000 cents back if it wins…substitute nickels, quarters, or whichever domination you like. Bet $9, win $10, bet $45, win $50, etc. The minus side is simpler; it’s what you win for every 1,000 whatever you bet, in this case 78 cents on the dollar.
You didn’t mention this, but another common bet is the over/under line. This one’s pretty simple, you bet on whether a certain stat will be over or under a certain number. Like spreads, the book wants as even a balance as possible, half points are possible, and the vigorish is in effect. Any stat can be used, but the most common is total points by both teams.
Of course, there are lots of other details like teasers bets and middling and parlays etc., but these are the basics.
Someone here who knows more about gambling than me can help you more. Anybody?