It depends on your state. Where the option is available, you should use your legalized betting options instead off the off-shore sites, even if it the cost is very slightly more (this isn't even always the case). The more transparency, the better and regulation and legislation seems to be headed in this direction in the US nationwide, finally. It took me years to recover a balance on Full Tilt Poker (which was a fair amount worth spending time on, though not life-changing).
The most common forms of betting are spread betting, moneyline and prop bets. I prefer moneyline, which takes away certain kinds of "bad beats", like Southern hitting a "significant to some" last second half court shot against Iowa in the second game of the year.
Spread - the team with a (-) is the favorite, (+) is the underdog. If you bet the underdog, you "give the points". If Iowa is a 2.5 point underdog and you bet on them, but Iowa only loses by 2, you win.
Moneyline - a little more confusing but the same +/- idea applies
Iowa +120
Illinois -140
The base figure is $100. If you bet $100, you get $120 if Iowa wins. If you bet $140 on Illinois, you win $100.
Prop bets- Sometimes expressed as a ratio. If Iowa is 10:1 to win the national championship, and wins, you get $10 for every 1 you bet. Often, this is expressed using the moneyline figure. So 10:1 is the same as +1000. If you bet $100 on Iowa to win the Natty, you get $1000 if they win.
A parlay means that you're simply making multiple bets at "double-or-nothing". If you do a four way parlay, you have to win all four bets to win. If you lose any of the four, you lose your wager. But if you do win all four, you win 8x your original wager (less the "vig"/house take) The house takes a bit of a bigger cut with parlays so most big money gamblers do not play these. They're more of a lotto ticket to win a lot of money on a small wager.