The long threaded rod along the bed was originally termed a "master thread" or "leading screw" but is now generally referred to as the "leadscrew". Any leadscrew needs to be very accurately made (they are often produced by specialist manufacturers, not the machine-tool builders themselves) with an Acme, square or other thread form optimised for the task - but never with a standard Whitworth or Metric form, as unfortunately found on many cheaper lathes from the Far East. The leadscrew will reproduce its exact pitch (hence the need for accuracy) on the material to be threaded - providing it can be driven directly in some way from the headstock spindle - usually by ordinary spur gears but occasionally by bevel gears or even, in a few cases, using toothed belts.
For everyday-use the changewheels are normally arranged to provide a very fine feed to the carriage; to set them for screwcutting means removing most or all of them and building up as fresh train following the instructions on a "screwcutting chart" that should be attached to the machine. At the end of the threading job the screwcutting train is removed and the fine-feed gears replaced. This time-wasting work can be largely avoided if a screwcutting gearbox is fitted -hence their popularity in industry. However, not even a full "quick-change" screwcutting gearbox can generate every pitch of thread and it is sometimes necessary to substitute changewheels to extend the range of the box - or generate metric threads from an English gearbox, or visa versa. Despite the attraction of a screwcutting gearbox for amateur use, where saving time is not usually as consideration, a lathe fitted with changewheels provides a much more adaptable machine.
If the lathe changewheel chart is missing all is not lost, the book, Screwcutting in the Lathe will help to calculate a fresh set. Further help can be found in a set of instructions for using changewheel calculators, and the necessary program downloads, can be found here.
Driving the cutting tools by a direct mechanical connection with the headstock also allowed, in ordinary work,  a much smoother and more consistent finish - and at the same time greatly reduced the fatigue suffered by the operator. This form of powered motion was originally called "self-acting" or "self-act" - and both terms were once widely used to distinguish between plain-turning and screwcutting lathes.
When the carriage is connected to the leadscrew some form of "nut" is used: either a solid nut, permanently engaged with the leadscrew, or either a single or double "clasp nut" that the operator can engaged and disengage at will. However, once the "clasp nuts" have been opened and the carriage moved back to allow another cut to be taken the problem arises of how to re-engage the nuts at the correct point--a problem solved by a simple but ingenious device, the "Dial Thread Indicator". The DTI consists of a gear engaged with the leadscrew but mounted on a shaft with a dial plate at the other end engraved with lines so the operator, by following charts (that vary with the pitch of thread being cut), can safely engage the nuts and continue threading accurately. Unfortunately, an interesting difficulty arises when cutting metric pitch threads on an English lathe - or vice versa - the leadscrew nuts cannot be disengaged and the lathe has to be "electrically reversed" back to a start point each time a new cut is taken.
Different Threads:
The first question that springs to the mind of the novice is: "Will my lathe be able to cut different types of thread?"  (Whitworth,  British Standard Fine, American National Coarse, British Standard Brass, American National Fine, British Standard Brass, Unified National Coarse, Unified National Fine, British Association, British Cycle Standard, Metric, etc.) The answer is, yes. Providing the lathe has the changewheels necessary to gear the spindle to the headstock so that tool moves the right distance whilst the spindle revolves once - it can be done. The 'form' or "shape" of the thread (which, simply put, is what makes the essential difference between the "types" of thread, not their pitch) is entirely in the 'shape' of the tool (or tools) used to cut it. The tool can be ground to replicate any thread angle at will; if you wished, for example, you could even invent your own; first however check this link or this one: they list and explain many of the threads forms both current and obsolete. Of course, not all is quite so simple, and at the end of this introductory article is a simple explanation of one of the confusing differences between metric and Inch threads.
A History Lesson:
The two engineers most closely associated with the development of mechanically-developed screw threads (although they did not invent the process) were both active in the 1800s: Henry Maudsley (1771 - 1831) "Machine Builder" of London, England (the "engineer's engineer") and one of his apprentices, Joseph Whitworth (1803 - 1887) Toolmaker of Manchester, England known for his plain-speaking not to say blunt ways (and probably the epitome of Shaw's dictum that "all progress depends on the unreasonable man."). Maudslay was the first able to make, and exploit, a very accurate screw thread. His masterpiece was a screw 5 feet long and 2 inches in diameter (1525 mm by 51 mm) with 50 turns per inch (50 per 25 mm) on which ran a nut 12 inches (305 mm) long with 600 threads. The apparatus was designed to average out pitch errors over small distances and was a vital element in the process of engraving the scale markings on astronomical and other very accurate measuring devices. Maudslay went on to manufacture a range of screwcutting lathes (using the principle of a "master thread" or "leading screw") examples of which can be seen in the London Science Museum and the Henry Ford Museum in Dearborn, Michigan, USA. Astoundingly, so accurate were Maudslay's threads (and so precise his measuring equipment). that he was able to observe the expansion effect of sunlight falling across one end of a leadscrew.
Whitworth was a toolmaker, engineer and millionaire businessman who brought a strictly disciplined approach to engineering. His design and development skills ranged across almost the whole field of mechanics but, following the publication in 1841 of  his: "On a Universal System of Screw Threads" he is best remembered for his success in standardising what at the time was a chaotic system of hand-fitted, non-interchangeable threads. He collected a large sample of screws from a variety of workshops and, having examined their properties, proposed a system whereby the ratio between the depth of the thread and its pitch was maintained over a range of sizes - and that the angle of the thread be 55 degrees. The system was in use in his own workshops by 1858 and was quickly taken up by other engineers as its benefits of simplicity and interchangeability - to say nothing of its recommendation by the greatest living British engineer of the day - became obvious.

Forming Threads by Hand:
It is possible to generate threads on a revolving cylindrical surface without using mechanical assistance by employing a "chaser". These look rather like wood-turning chisels with a "thread form" cut into their end or side faces and are made from hard steel - tool steel for the finest-quality ones - and vary in width and thickness according to their thread pitch and job they have to do.
The full-sized type are normally fitted to stout wooden handles to give the necessary purchase (which can be considerable) and are expensive. However, there is a cheaper alternative, the chasers that come from automatically-releasing die holders; these units are used on capstan lathes and hold 4 small identical sections of tool steel formed with a very accurate thread along one edge. If these are removed and mounted in a suitable metal  holder they can be used exactly like their full-size cousins. Unfortunately,  using either type is difficult and beginners are well advised to avoid them completely - although they can have a role to play in "cleaning up" a mechanically-cut thread and imparting a radius or other shape to the crest and root of the thread, a process not possible with the single-point thread generation method described above. In use the chaser is rested against a suitable support - with some lubricant between the two - and fed into the workpiece on centre height with a steady sliding motion..

Whitworth thread form with 55 degree angle and rounded roots and crests. Other threads have flat crests with rounded roots, or visa- versa, or both crest and root can be flat. The angle can also differ - standard metric threads are 60 degrees - whilst some threads are "square cut" at 90 degrees. Whilst the "single point" tool commonly used in a lathe to generate thread can cut the angles correctly it cannot generate the radii at root and crest and these are sometimes formed post machining by the use of a hard steel "chaser".

An essential part of the screwcutting toolkit - a threading gauge marked with the common thread angles. This allows the tool to be set "square" to the work, as illustrated below.

Using a thread gauge to set the tool for internal threading. The gauge is held against a plate pressed against the accurately turned end of the tube which is to be threaded.

The cutting edge of an external chaser.

With skill (and luck for the beginner) the chaser will bite into the surface and begin to form a spiral cut; as the other points on the chaser engage with the spiral, the action becomes, to an extent, self-stabilising and easier to perform; many passes are normally required before the full depth of the thread is generated.
How was the first accurate thread generated? Take a wooden rolling pin and place it on a flat surface. Pick up a knife, hold it horizontally and press the end of the blade onto the top of the pin near one end. With the knife twisted  through 10 degrees or so, press down and use it to roll the pin away from you. As the pin rolls a spiral line or "thread" is generated  - and all it needs is deepening out into a V shape to complete the job. Unfortunately, unless you are the cook in house, you now in dead trouble with SWMBO.
An interesting difference exists between "English" threads (a definition that includes American types) and Metric. English and Metric Threads
All English (sometimes called "Imperial") and American threads are based on what happens within the boundary of a single inch. Inside that inch length you might have any number of pitches - though typically restricted to a range extending from 4 to 56 t.p.i . Metric threads are arranged differently, there is no fixed length into which they must fit and each has a pitch fixed as a fraction, or multiple of, a millimetre. The effect of this is illustrated if you take the centre of a valley anywhere on an "inch" threaded rod and measure one inch in either direction: the finish point will also be in the centre of a valley--even if the thread is something ridiculous, like 23.5 t.p.i. With metric pitches arranged so that the valleys centres are a fixed distance apart in millimetres - for example 0.25mm, 0.75mm, 1.0mm, 1.5mm, 2.5mm, etc. - if you measure as for the inch threads, but using a fixed unit of metric length (such as 100mm), you will find that whilst some pitches end in a valley centre, most do not - because they don't divide exactly into 100. Whilst for all practical purposes this difference between the thread types does not matter it does creates an interesting effect when screwcutting for, whilst just a single gear is needed on the thread-dial indicator of an English lathe, on a metric machine three are often fitted to cover the range of common pitches and up six would, in theory, be required to cover every likely requirement.