You should start by developing a few puppet forms and getting used to using your hands to create shapes and characters. Find a dark place and set up a light source. You can use a candle, a lamp, or even a bonfire. Be sure you have some kind of surface to project your shadows onto. Bear in mind that a surface that isn't flat will distort your puppets, so choose a surface that is shaped to your liking. Invent a few puppet forms. Simply place your hands between your light source and your projection surface and begin making shapes and moving them around. Shadow-Puppets.com has plenty of examples that can get you started including a camel, a goose, a deer, a grandpa, a bunny, a bird, a goat, and a dog.
Once you've invented some characters and you're used to moving them around and making them seem expressive, you can invent your story. The narrative you convey through your shadow puppets can be simple or complex, comedic or dramatic, brief or as long as you want it to be. You can create a story that's told only through movements and interactions between different characters, or you can write dialogue and give voices to each of your characters. Let your characters take on lives of their own. If you're using more than one character, develop ways for them to interact.
When your story is thoroughly prepared (whether you've got it memorized or written down), you can start setting up your recording equipment. Get your digital video camera and aim it at the surface you're going to project your shadows onto. Put it on your tripod or have a friend hold it. Make sure your camera is behind your light source and be sure your actual hands won't be visible in the frame. Practice a few of your puppets on the screen and make sure you've got your frame lined up so you've got enough space for whatever interactions are going to take place in your movie. Be a cinematographer and put some care into your frame.
Once you've got your equipment all set up, you can record your movie. If you've got everything memorized, you can go ahead and do the whole thing in one take. Don't get too nervous about making mistakes, because you can always start over again. If you've got your camera on a stable tripod, you can even stop recording when no puppets are on screen and then start recording again to produce the illusion of seamless continuity. If your camera has a microphone, you can record dialogue and even sound effects on the spot. If not, you can always edit dialogue or sound effects in later using a microphone on your computer and your video editing software.
After you've shot all the footage you need for your video, you can capture the footage onto your computer using your video editing software (Imovie, Windows Movie Maker, Adobe Premiere Prop, Final Cut Pro). This process will be different depending upon what kind of camera you use. You'll likely use a USB cable or a Firewire cable. Consult your camera's instructions or user's guide if you need help getting your video onto your computer.
Once you've captured your footage, you can use your video editing software to edit it. You can cut out bits and pieces that you don't like or rearrange the order of your story. If you've got a microphone for you computer (or if your computer has one built in), you can record sound effects or dialogue and include them as well. Fine tune your movie to make it tell your story well. You may even want to add an opening title, ending credits, or some dialogue title cards to produce a sort of silent movie effect.
Once your movie is finalized and everything looks and sounds the way you like it, you can export it as a video file to be watched on your computer. If you have DVD authoring software, you can import your video file into the program and burn a DVD to show to your friends and family, or even to strangers.