Photography basics haven't changed since 1826, when Joseph Nicéphore Niepce recorded the first photograph. Niepce's invention was simply a variation of a centuries-old novelty device called the "camera obscura"---a wooden box with a lens on one end and a ground glass on the other end on which the operator projected images. To make your own photograph enlarger, simply put a camera obscura on a vertical stick and shine a light through it.
Finding the Camera Head
For the "camera obscura" enlarger head, find a camera with a bellows---an apparatus that dates back to the early days of photography. Shop for a bellows camera on eBay using its "Search" function, or check antique stores, garage sales and rummage shops.
Building the Vertical Stick and Base
Next, build the vertical "stick" to which the bellows camera will attach. The bellows camera will have a threaded hole on the bottom that normally connects the camera to a tripod; use that threaded hole to attach the camera to the stick. Purchase the materials for the stick and base at a home supply company, or, if possible, salvage them from old items you have around the house and garage. You will need a 1-by-4-inch-by-5-foot board for the stick and a 3/4-inch-by-20-by-24-inch board for the base. Cut a 1/4-inch slot down the center of the 1-by-4-inch board,so that the bolt attached to the camera can slide up and down the slot and tighten with the wing nut. Attach the board to the 20-by-24-inch base by drilling three holes into the 3/4-inch side, and attach 3-inch wood screws to tighten the unit together.
Final Details and Use
To convert the bellows camera to the enlarger head, remove the back, measure the opening and construct a wood frame that will accept a homemade negative holder and a light shade that will sit on top of it. For the negative carrier, use a piece of mat board or plastic sheeting cut to the dimensions of what size negative you plan to use in the enlarger. For the light that will sit on the back of the camera, check what you have around the house---a small floodlight with a vented metal dome will work, or a modified tin coffee can with a hole cut in the base and light socket inserted will also work. Once you have resolved all these details, put the enlarger through a test run and work out any bugs.
To operate this homemade enlarger, place a negative into the carrier, insert the carrier in the enlarger and set the light fixture on top. To view your projected negative, loosen the wing nut and pull the enlarger head down the stick until you've projected the image where you want it. Tighten the wing nut, then make your fine adjustment by pulling the camera bellows down until your image comes into focus. Make more than one of these simple homemade "camera obscura" enlargers if you need enlargers that take different-sized negatives. Like Niepce's first camera, you'll find them simple to make and simple to use.