The earliest method involved simply twisting the fibres with the fingers/hands, but this was very time-consuming and inefficient, and produced a thread that was generally not very strong. It also was pretty nasty on the fingers - especially with rough fibres like hemp. This technique, however, is still employed by some native tribes in the world - for example some of the Australian natives spun human hair for various purposes using this technique.
Whorling / drop-spindle
The next and most prevalent method was called "whorling" and involves the use of what is modernly called a drop spindle. This device consists of a hooked shaft (called the spindle) with one end fastened to the centre of a disk.
The spun thread is looped around the shaft and tied to the hook, then is held by the spinner in one hand. The spinner then spins the whole spindle, with the disk acting as both a weight to keep the spindle turning, and a place to rest the spun thread upon.
Fibres are added to the thread the spinner holds in her hand, and twisted into the previously spun thread. This creates the thread, and as it is completed, the spinner lets go of the thread and adds some more firbe to the top. the spindle thus slowly drops to the floor (thus "drop" spindle).
When the spindle reaches the floor. The spinner stops the spinning and unhooks the thread from the hook and winds the completed thread onto the shaft - the re-hooks it and continues from there.
The spinning-wheel made its appearance only late in period and at first was just a drop-spindle turned on its side and added to a large fly-wheel. The fly wheel was heavier and thus could be kept spinning for longer.
The spinner could also walk backwards the entire length of a room, drawing out the thread and keeping just ahead of the "twist" in it, rather than be stuck with just her own height. This was called the long draw method and the thread produced this way was not of as high a quality as that produced with a whorler - and thus whorling remained important for a very long time after the wheel was invented and put to use.
Early spinning wheels did not self-wind onto the bobbin (the shaft of the wheel's spindle as previous), as modern wheels do - the spinner still had to stop the wheel and wind the completed fibre onto the bobbin by hand.
An interesting point to note was that the spindle on these early wheels was often quite sharp, and thus sleeping beaty could quite easily have pricked her finger upon one - a task nearly impossible on modern-day wheels.