As I am still a beginner myself, I have indeed heard of the rule "Don't waste a pawn or other piece just for free". It seems to me that classical openings such as, of course, the King's and Queen's Gambit, are "created" by very experienced chess-players, maybe even grandmasters, I don't know. But I do know, that if an experienced chess-player SEEMS to waste a pawn or piece, there is often something more behind it - like advanced tactics, for example. I have seen this is at least two tutorial video's right here on Chess.com, though I'm afraid I cannot tell you which video's those were at the moment. Try going to the Video Lessons at the top of the screen, then click on Video Guide to the left - there you will see all video's categorised by theme, such as beginner, openings, tactics, strategies, endgames, and so on and so forth. I'm almost certain that the video's I spoke of were in the Amazing Games for Beginners section, so just scroll down and you should find it. I hope that helps you out, because I can't say I know many openings, including Gambits, that well yet. 
What's the point of a gambit?
Normally, central control, or to develop pieces quickly and attack.
If you look at the queens gambit accepted 1. d4 d5 2. c4 dxc4 3. d4
White has an ideal pawn centre (e4 and d4), is attacking the pawn which is difficult to defend without weakening your position.
Or 1. d4 d5 2. c4 dxc4 3. Nf3 Nf6 4. e3 you probably wont be holding on to the pawn.
The King's gambit I've never played and someone will explain but I think the idea is quick development and an attack on the king who will probably have difficulty getting to safety with that pawn structure.
If you are going to play a gambit, you should understand the ideas behind it, otherwise you ARE throwing away a pawn for nothing.
A true gambit is designed to encourage your opponent to waste time while you grab a lead in development. Sometimes it causes him to move a piece a second or third time, thus delaying his development (such as the Evans Gambit). Sometimes it causes him to move a piece into a less-than-ideal position that can be exploited. Sometimes (such as the King's Gambit or the Benko Gambit), it opens files to get your Rooks into the game early.
Most gambits are for the White player for good reason... delaying Black's development amplifies the advantage of having the first move.
The Queen's Gambit is kind of its own animal, but then I don't consider it a true gambit since the pawn is easily recaptured at White's leisure. In fact, most Queen's Gambits are declined since it's so hard for Black to hold on to the extra pawn.
Well, the point is that in gambits, it's usually calculated so that the player giving away the pawn has compensation. In chess we say we have compensation for a sacrificed pawn when there is counterplay: i.e. a means of putting pressure or attacking an opponent. It is about long-term play. That means that the player taking the pawn will usually spend the rest of the game defending and trying to hold on to the pawn, and the other player will attack and try to win the game or just get an advantage.
So, gambits are for aggressive players who like to attack their opponents a lot. They're here for players who say: I wanna win or lose, no draws!
Take a look at this game Nakamura - Andreikin. In case you don't know Nakamura, he's one of the top 10 chess players in the world and the #1 US chess player. He's considered the mad man of top chess, playing all kinds of irregular openings. In the game he first plays the kings gambit, sacrificing a pawn and shortly after he plays the Muzio gambit, even sacrificing a knight!
Here's the power of a gambit. I hope that is clear now. Mind you, it was a blitz game and the position is very, very complicated. Therefore black's position is very hard to defend in a short time while white's is easy, attack! Gambit's aren't very effective in 2hours / 40 moves games, because black can usually find the correct moves, but in shorter time controls, they are very well playable!
I am studying gambit positions: king's and queen's. Now, I will admit that I am still a learning chess player. One rule that I have heard mentioned left and right across chess.com for noobs is "Don't give away pawns or any piece for free." I take this rule as a fact- a simple no brainer. However, the king's gambit, as well as the queen's gambit, seems to defy that logic. Moreover, if one looks at a simple game: 1.e4 e5 2.f4 exf4 3.Nf3 g5 (which can be found @ http://www.chess.com/explorer/index.html?id=96&ply=3), the king's gambit accepted, the pawn is well defended and doesn't seem to be lost anytime soon. I know professionals explain that the gambit is to make the opposing color's center weaker but is having a pawn disadvantage really that necessary? Can someone explain this to me, as I am desiring to learn more about chess?
Thank-you
(P.S. if you ever want to play chess, rated or unrated, message me.)