The simplest way to build a Wi-Fi range extender involves taking a piece of foil or foil-backed paper, forming it into a roughly parabolic shape, and attaching it behind the router's antenna. If the router has more than one antenna, build a range extender for each one. This type of extender only improves signal strength in the direction the parabola opens in, and it actually decreases signal strength behind the extender.
While foil and paper are the easiest materials from which to make this kind of range extender, virtually any roughly parabolic item works. Remove the bottom of an aluminum soda can and make a vertical cut down its sides to make a range extender that easily fits onto most router antennas. A slightly more involved method uses parabolic strainers and cooking utensils and places either a router antenna or a USB network adapter near the parabola's focus point.
All of these Wi-Fi extenders generally only increase signal strength along particular lines of sight, as they do not electrically boost the router's native signal at all. Because of this, these types of Wi-Fi extenders do very little to improve signal strength for devices near the router or for devices not directly in the extender's line of sight. However, these devices can significantly boost signal strength at long distances with clear and relatively direct lines of sight from the router.