First popular in the 50s and 60s, teardrop trailers are light weight trailers designed to sleep one or two people and can be towed by anything from a light truck to a sedan, I even spotted one being pulled by two motorcycles. They get their name from the teardrop shape round at the front and tapered to the back, to lower wind resistance. You can purchase one for around $5,000 but there is generally a wait because most all companies that make them only make them to order or short production runs. However, you can save a lot of money by building your own teardrop camper trailer.
The first thing you will need is a good solid trailer. This needs to be large enough to attach the base to, generally 4' x 8', but you can go larger if you feel you need more room. It's best to buy the trailer because they must be street legal. Luckily this is about the only part of the teardrop camper that is under strict guidelines, everything else about the teardrop camper is only limited to what you can imagine and build. Take note on the trailer of an holes going through the frame so that you can use them later to bolt down the foundation of the teardrop camper to the trailer. Also note how much the trailer is rated to carry and its own weight, this way you can compare it to your vehicles towing capacity.
Next decide what you want to build the teardrop camper out of. Traditionally, teardrop campers were made out of aluminum because of its abundance after WWII, but most recently built teardrop campers use primarily wood. It doesn't matter what you use as long as it's a material you are familiar with and can fabricate easily, which is why most go with wood. You start by roughing out the foundation of the camper, made just like a floor would be in a home accept the "joists" are only 2 feet apart. Then clamp two pieces together for the walls and draw, cut, and smooth out the shape of the teardrop, this way both sides are identical. It is important that whatever material you do decide to build the sides and the top out of, you are able to water proof it.
Now, you want to take a minute to draw out what you want as far as shelves, counters, cubbyholes, and drawers. These additions will also provide the straight edges for you to attach the sides to. Then add stabilizers as needed so that the whole thing doesn't go floppy on you in the wind. Then add doors and windows, a big hatch-back style door for the rear area, and water seal everything.