I have trouble with learning what pieces to sacrifice when. Any good examples or playable scenarios on the web to help guide with that? My biggest problem is in the early game, learning what to sacrifice to move pawns out of play so I can move other pieces up the board. Any assistance would be appreciated.
A sacrifice made at the beginning, with no clear and immediate advantage, is called a gambit.
There is no hard "rule" for when a gambit is worthwhile or not; it all comes down to what imbalances it gives you, and whether you think you can use those to your advantage.
For example, in the Danish Gambit (accepted), white sacrifices two pawns, hoping the extra space/development he gains will help mount an early attack. In the Queen's Gambit (accepted), on the other hand, white sacrifices the pawn knowing he will either get it back, or black will have to severely weaken his position to hold onto it.
I look at a sacrifice as an "exchange in disguise."
For example, you have a (castled) rook on the open f file, which you "sacrifice" for the knight on f6. Technically it's a sacrifice of 5 for 3. But maybe that knight is a key defender and Black is helpless without it. Also, if the rook is recaptured by the g pawn, that alone, is worth the sacrifice, because you've removed the f knight AND g pawn (now doubled on the f file) for "only" the rook.
What you are referring, my friend, is called gambits. They are done for achieving a better position by giving away a small piece like pawn. Usually, when the player offers a gambit, it is up to the opponent to accept or reject the play.
Sacrifices are generally made by sacrificing material for a positional and dynamic advantage. In the optimal scenario, a sacrifice is used for a mating net, as shown by many checkmate puzzles.
The best ways to learn sacrifices would be:
Learn a gambit. Probably not Queen's Gambit, since in the majority of cases black will decline it. Most other gambits would be fine to learn from though. Be very wary of gambits that rely on the opponent not knowing how to play the gambit. This will not teach you much, as it relies on the opponent making major mistakes. Danish Gambit or King's Gambit are good for learning the concepts behind sacrificing for white. Black has less advantage when using Gambits, but you could look at a few that you like. Remember that each gambit has a different playstyle that goes along with it. The Latvian Gambit generally supports very aggressive play, while other opening's might consider this to be overextending.
Learn the concepts of sacrificing. You are giving away material to gain space and momentum. In most cases, you should avoid trading away pieces, as this gives the opponent breathing room and loses your momentum. By maintaining a threat (such as a Bishop pin on a Knight-Queen) you give yourself room to do other things, while limiting what they can do. If the game drags out, your material disadvantage will become more apparent. Losing 1 pawn to allow your pieces to have more freedom when is less concerning in the opening than in the endgame.
Understand the relative worth of pieces. A rook that remains in the corner is worth less than 5 and a knight in the middle of the board that controls a lot of the board is worth more than 3. Also note that this can change rapidly. Is that rook able to easily obtain an open file? Or can that knight be easily kicked from it's square. These are all things to consider when sacrificing pieces. Giving up a rook for their powerful knight might be a worthwhile sacrifice.
Look at some games of the top grandmasters. The top games of grandmasters considered to be tactics-based such as Fischer or Kasparov are good to look at, even for interest's sake. Kasparov was known to be brilliant with his dynamic style because he was very good at the opening and middlegame. So have a look at some of their games and try to understand the reason for sacrifices they make. A number of Petrosian's top games involve him exchanging a rook for a bishop. Note that not all their games involve sacrifices.
Know that you shouldn't sacrifice all the time. Most of the time, the right choice will be to keep your material. At a lower level, it is harder to maintain a dynamic advantage, and at a higher level, they can often defend against your advantage. It is a really hard skill to develop.
Sacrifices generally have a bigger advantage in shorter time controls. The opponent has less time to react to your threats, and at the very least, gives you a short term advantage and a good chance for them to make a mistake. Giving up a bishop for the pawn on h2/h7 can give your opponent a lot of panic in a short game, but given time it is generally easy to defend. I personally try to avoid this, because it leads me to have bad habits in games with longer time controls, but it does work better in shorter games.
Good luck with learning sacrifices. There are a lot of things to think about but overall, just do what you feel is good and have fun.
EDIT: Fixed typo