Breathe from the diaphragm. In order to project correctly, you must breathe from your diaphragm. Your diaphragm is a thin muscle underneath your lungs and above your intestines that sits like a sheet across your midsection. When you use this muscle to control your breathing, your breath will be deeper and more supported, and your sound will be loud and not strained. If, when you inhale, your shoulders rise and fall, you are not breathing correctly. Put a hand on your stomach and breath in, letting your stomach distend as you take in air. Your should feel the sensation of a deep, supported breath and you shouldn't have to use your shoulders at all. Your shoulders should be relaxed, in fact. Now breath out, letting your diaphragm and stomach muscles do all the work, focusing on letting the rest of the body relax.
Come on to a supported voice. Start by humming, using the supported breath to sustain the hum. After you have done this for a couple minutes, let your jaw fall slack and go onto an "ah" sound. Don't force it now, and don't focus on how loud the sound is. Instead, focus on how intense the sound is. Visualize the sound as a focused beam of light. Start exploring the range of your supported voice. Begin doing an easy vocal slide, starting low in your register on an "ah," then sliding up into your falsetto, then back down. Take your time, and don't worry about breaking between your falsetto and chest voice. This is not performance time, this is YOU time. Finally, come on to a more staccato "ha, ha, ha, ha" sound. Let the diaphragm and stomach muscles do all of the work, pushing each and every one of the "ha's" out.
Focus on projecting supported voice. Begin a hum again, going into an "ah," as before. This time, however, when you take in your breath through use of your diaphragm, let it drop in, then use your stomach muscles to lift and support the air as you go from the hum into the "ah." It shouldn't be as forced and rigid as if you were preparing to be punched in the gut, but there should be some muscle tightness and flex action. That being said, the rest of your body should be absolutely relaxed. As you flex these stomach muscles while you make your warm up sounds, you should begin to hear a notable difference in the volume of your "ah." It will increase in volume, but not in a forced way. It should be a fuller, richer sound that could fill any auditorium or large room, no matter what material you are performing.
Use the diaphragm projection technique in the real world. Practice coming on to your supported voice every morning. It's a sensation that does take some time getting used to, and practice will make it feel like second nature. When you rehearse your piece, whether it is sung or spoken, take the time to focus on your breathing. It may not feel natural or organic at first, but the more you incorporate it, the more natural it will become, and soon you will find yourself breathing and performing using the supported diaphragm breathing technique without any thought at all!