Most of the time your opponents won't allow you to win with such basic tactics such as a simple fork but if you look deeper into a position you may be able to find a combination which may not be so obvious. A combination is a forced sequence of moves involving a sacrifice. It is always important to calculate checks & captures to see if they work, and threats.
This is a good example from CT (Chess Tactics) Art 3.0. Here we calculate that the check works. Visualizing the pieces move around the board is an important skill you need to develop. You will see the theme of removing the defender here with a sacrifice. Then finally it will end with a skewer. White to move. Enjoy.
What would you do if it's black's turn?
The worst feeling in the world comes when you loose your Queen with no compensation. The reason it's so important to get good at tactics first is that you can play great strategically when tactics are not possible on the board, but then you loose the whole game because you missed a tactic and your opponent saw it. But before you get CT-Art 3.0, you may want to consider having a hard copy of a tactic book by Seirawan called Winning Chess Tactics. It will show all the basic tactics and knowing them and having it as reference in the book will help you solve the tactical problems in the program. I believe there are over 1200 tactical problems in the program and there is even a pocket pc version of it which makes me wish I can afford a pocket pc right now. If you are a beginner and extremely tactically challenged, then get the Seirawan book and Chess Tactics for Beginners from Convekta. Solve those 1200 problems about 7 times so that you really get the hang of it. Then move on to CT-Art 3.0 and spend about an hour a day for the rest of your Chess playing life if you can afford it.
If you are good at tactics, the next step is to learn the Middlegame. I recommend Jeremey Silman's Reassess Your Chess first because it's a bit easier to digest amongst other intermediate to advance books such as Nimzovich's My System and Kotov's Calculate like a Grandmaster.
Jeremey Silman has a good endgame book also called Complete Endgame Course. They say that the fastest way to learn the game is to learn it in reverse; meaning learn the Endgame first. This is not relevant if you can't get past the first 12-15 moves without loosing a decisive amount of material though, so learn those tactics well and middle game next, then endgame.
Lastly, for beginning Opening study; Ideas Behind the Chess Openings by Reuben Fine is a good start, Modern Chess Openings (MCO) is good reference, and I believe if you realy get into it then Chess Informant has a huge series in print and on CD called Encyclopedia of Chess Openings that you can study in depth. I like to specialize because there's no way you can learn every opening. It's important to learn how to play 1.e4 and 1.d4 games for both white and black.
Take a peek at the Ruy Lopez and Sicilian Najdorf so that you have a basic idea of the most practical openings with 1.e4 and perhaps a 1.d4 opening like the Modern Benoni and Queen's Gambit. Then practice Tactics! Then Middlegame for strategy. Then Endgame, and lastly Openings.
Work hard and Good Luck!