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.
Long Draw Method
The spinning wheel only made an appearance very late in period, and was basically just a whorler/drop spindle turned on its side with a fly-wheel attached. The technique employed for wheel-spun thread was called the long-draw method and involved walking backwards creating thread just ahead of the already-twisting part of the thread (ie drawing the thread out a long way as you walked).
The thread created this way was not as strong as the traditional (at that time) whorl-spun thread. This was mainly due to the lack of worsting and less attention-to-detail that could be paid as the spinner moved quickly backwards. It was also meant to be a quickly-produced thread.
This produced a rather interesting turn of events that stated that wheel-spun thread was illegal to be used as the strong warp threads in a fabric - which had to be replaced by the stronger whorl-spun thread. It could be used for the weft or decorative use, but anything that needed strength was not recommended.
Whorl-spun thread was thus used for quite a long time after spinning wheels were invented and put to use.
Whorling / drop-spindle
The next and most prevalent method was called "whorling" and involves the use of a whorler (or what is modernly called a drop spindle). This device consists of a simple, pointed shaft (called the spindle) with one end fastened to the centre of a disk (the whorl).
The spun thread is securely looped around the shaft and hooked over the top, then is held (a few inches away from the spindle) 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 (by undoing the loop at the top and rotating said spindle).
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 fibre to the top. the spindle thus slowly drops to the floor (thus why "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 - then re-hooks it and continues from there.
Another type of whorled spindle is the support spindle. This often looks very similar to a drop spindle in many respects. It consists of a central shaft which may be made of wood or metal and a whorl, placed near the bottom of the shaft. The whorl may be a disk, knob or bead which gives weight to the spindle and provides a resting spot for the spun strand. The bottom of the shaft is pointed to allow it to spin more readily, and the top may be hooked, but may also be pointed. A low-whorl drop spindle can be used as a support spindle provided the bottom has a point to it, and many support spindles can be used as drop spindles, provided they have enough weight to them to allow them to spin. In these cases, the difference is not the actual configuration of the spindle so much as the technique the individual spinner uses.
The pointed bottom of the spindle is rested on some surface which may be the lap, the ground (if the spindle is very long) or a "spinning bowl". This is a small smooth surface such as a small wooden bowl which allows the spindle to spin faster and longer than it otherwise would. Fibre may be hand-spun and attached directly to the shaft of the spindle, or a spinner may use a leader thread. The unspun fibre is held and drafted with one hand, while the other hand spins and supports the spindle. The shaft is given a fast twist and allowed to spin on the spinning surface while the spinning hand gently supports it. The idea is to keep the spindle from falling over while allowing the spindle to spin as long as possible. When the spindle slows down, another spin is given, and so on and on.
As the fibre is twisted, the spinner drafts out additional fibre. When the strand reaches arms length, the spinner winds the spun thread onto the shaft and continues drafting and spinning in this manner.
Support spindles may be used for any type of fibre, but are very useful for fine spinning such as cotton or silk thread, where the weight of a drop spindle could break the thread in progress.
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.