The Elizabethan farthingale is a hooped petticoat worn to give the skirt its distinctive shape as seen in paintings of the high-to-late renaissance period. It came in two basic flavours: the Spanish, or conical farthingale, and the wheel farthingale, sometimes called the English farthingale.
The Spanish farthingale is probably easier to construct, with as few as three hoops of varying sizes inserted in a stitched casing on the petticoat.
The wheel farthingale is a more complex garment to construct effectively since the intention seems to be to make the skirt stand out horizontally from the waist before dropping precipitately to floor length. The images of the period aren't particularly helpful in determining the shape of the wheel farthingale but practicality (did the Elizabethans ever bother about that?) would suggest that the supporting structure should be more elliptical than circular.