A megaphone is very simple to make, because it's essentially a cone. The shape of the cone is what projects and amplifies the sound. You can make a homemade megaphone easily by taking or making a cone with its small end large enough to speak into. If you want something more advanced, you can connect a microphone and other electronics to the cone to help amplify the sound even more.
Take a square sheet of poster board measuring at least 25 by 25 cm (10 by 10 inches) and wrap it into a cone. Look for sturdier material if you're going to attach electronics, like lightweight cardboard. You can also cut the spout off of a plastic funnel, but use caution with the needed tools.
Tape the cone together, making it as large as you can, and trim the large edges to make it close to an even cylinder. Then, snip off the pointed end for a mouthpiece. You can wrap more poster board around the large end to make it bigger if you want. Stop now unless you want to add the electronics.
Attach a small stereo speaker to a microphone using a stereo coaxial cable. You need a speaker with its own amplifier and power supply, like one that hooks up to an MP3 player. Insert fresh batteries into the speaker.
Connect the speaker to the megaphone's mouthpiece end so the speaker sound will travel through the megaphone. Place as much of the speaker's output end within the mouthpiece -- cut around the mouthpiece to make it bigger if needed -- then tape the two together, wrapping the tape all the way around so all sound goes through the cone.
Tape the microphone and cable to the bottom of the megaphone assembly so the actual microphone is at the end with the speaker and mouthpiece. You can choose to leave the microphone and cable free and not taped if you prefer to hold the microphone in one hand and the megaphone in the other.
Turn on the speaker and speak into the microphone. The sound from your voice will come out through the megaphone in an amplified state.