Lifters are also called ionocraft, but the original name for the three sided, aluminum foil craft was lifter so I'll call it that most of the time.
The lifter is a typically triangular shaped, lightweight device capable of lifting its own weight. However, it cannot also lift the weight of its high voltage power supply that powers it. The basic components are two conductive electrodes, one having a sharp edge (usually a very thin, bare copper wire on the order of 30 to 50 AWG/gauge), and the other having a smooth edge (usually aluminium foil.) The rigid structure is typically make of very thin balsa wood sticks (around 2mm or 1/16" thick) or straws. Glues such as krazy glue (filler type) or cyanoacrylate are very effective for holding it together while not requiring much and also being lightweight.
Voltages needed to power it are typically 20kV and higher. Most experimenters use a modified computer monitor as the high voltage power supply as most are capable of supplying around 28kV. Note that the power supply must also be able to supply a useful amount of electrical current since the top wire will be either leaking or collecting electrons as it ionizes the surrounding air. This requirement means your average Van de Graaff generator or Wimshurst machine may not be able to make it fly since they supply only low microamps of current.