Projection is ultimately an issue of resonance. You're not talking louder, just fuller.
Lay on your bed with a heavy book on your torso right at the point where the rib age meets the belly. Take a few minutes of breathing through your nose to direct your breath in toward the point where the book is at. If you do it correctly, it will rise evenly. This means you're using your diaphragm for all the work. The diaphragm is a membrane connected to the lungs that lowers toward the solar plexus when you breathe in and pulls the air into your lungs.
At first, this is going to feel unusual. When most people breathe, they try to expand either the stomach or the chest (usually the latter). Using the diaphragm to its fullest, you're taking in air more efficiently and thus getting much more oxygen to your brain. This might result in an initial feeling of light-headedness, but if you make this a habit it will become normal and effects like that will stop.
Let me take a moment to say that this type of breathing is also beneficial for the above said reason that it increases oxygen flow to the brain. This helps keep you much sharper, more alert, and able to think faster. It also helps when exercising because it allows your cardiovascular system to more effectively distribute oxygen to the muscles so that they don't tire as easily.
Now that we've got the breathing down, resonance is the next step. There are three key places to resonate, though I only recommend two.
The first is in the crown of the head. Women are generally able to achieve a proper head voice more easily than men, though guys with a tenor range can generally pull it off without too much trouble.
The second is in the nasal cavity, also known as the mask. Singer try to avoid this because it's hard to maintain melody when doing it. Your voice tends to get stuck in a very limited range, and often goes flat. Very few have the type of voice that sounds good resonating from the mask, and most of them are in public speaking.
The third is the chest. This one is natural for most men as the baritone range is the most common. I have a bass/baritone range so I tend to speak almost exclusively from my chest. At deeper levels, the voice actually tends to rumble a little.
To resonate, you first have to relax the throat and vocalize a single vowel. Take a deep breath and just vocalize an "ahh" sound for as long as you can. As you're doing this, place one hand on your chest and one on the crown of your head. Relax the muscles in your head, neck, shoulders, chest, and back until you feel one of the areas begin to vibrate. That's resonance. Try to harmonize at a pitch you feel comfortable with and find which area resonates first or best. That will give you a rough idea of where your range might lie.
Resonating is going to feel weird at first, but just as with the breathing exercise it will feel normal after a little practice. Once you can resonate with little trouble, start practicing it with sentences. Start making it a habit. You'll notice that it takes considerably less volume for your voice to fill a space and you have a more authoritative tone. People will be more inclined to take you seriously.
To project to a large crowd, apply the same principles and image trying to throw your voice so that even the people in the cheap seats can hear it. You'll find that it actually requires very little in the way of extra volume or extra expenditure of air.