To obtain a complete picture of how Sunspots develop, it's important to understand the Sun itself: how heat is generated and transported through the Sun's different layers, its rotation, its magnetic field and its surface.
The Sun is a huge, immensely hot circular concentration of ionised gas; gas that contains electrically charged Atoms known as Ions. The immense heat of the Sun is generated at the Sun's core, where temperatures are at 15 million degrees, cause atoms to disintegrate, revealing the elements within: electrons, neutrons and protons. Neutrons are electrically neutral; they do not interact with their environments so escape through the core fairly easily and rapidly; protons and electrons are electrically charged: protons positive; electrons negative. The core of the Sun is so hot and the materials are so compact that thermal energy within the elements increase to the point where their movement within the core is increased substantially to the point where they are continuously colliding, leading to the process of nuclear fusion. The heat that is generated within the core needs to be transported from the core to the photosphere: the surface of the Sun. The area surrounding the core is called the radiation zone, , where heat is transported through the zone using radioactive. The means of transport through the radiation zone is by a complicated means of transferring heat between Ions. Ions can exist in this part of the Sun because whilst the temperatures are still immensely hot relative to humans, they are cool enough to allow atoms to remain intact. There is no set path through the radioactive zone, so it can take thousands and thousands of years for heat to complete its journey through the radioactive zone. The heat enters a much cooler layer known as the convection zone. The temperature in this zone is at 2 million degrees, 3 million degrees cooler than the radioactive zone. Because of this, radiation is not a suitable means of transportation because if radioactive was used at 2 million degrees the atoms would move even slower and the Ions would not transfer heat between each other so readily. A new mechanism must be used to help move the ions through the convection zone to the surface of the Sun, and this mechanism is known as convection. Convection is the process of moving or transporting heat through non-solid state entities such as gas or liquid. This is achieved, in its basic form, by hot material rising to the surface, releasing the heat, cooling, and then sinking back down to the bottom of the convection zone. When the material heats up, it rises to the top again: it's almost like a circular motion. There is a set path through the convection zone to the surface of the Sun, and because of this it takes just a week for heat to rise to the surface of the Sun.
The Sun's magnetic field is generated by the movement of the hot ionised gasses within the Sun. The Sun's magnetic field is different to that of Earth's magnetic field: with Earth's field, it is the simple, conventional North-South pole magnetic tube; the Sun's magnetic field, however, is a contorted mangle of magnetic field lines leaving and entering the Sun and in a huge number of different locations, as opposed to the simple North-South pole attraction. As can be imagined, the Sun's magnetic field is very complex and is not yet fully understood. It is known, however, that one of the reasons for the Sun's contorted mess of magnetic lines is due to the nature of the Sun's rotation. Because the Sun is completely made of gas and hot plasma, different sections of the Sun complete a revolution at different times, known as differential rotation.
The nature of the Sun's revolution, therefore, contorts and tangles the magnetic lines of the Sun. The behaviour of the magnetic field is also influenced by the convective motions of the convection zone. Both the differential rotation and the convective motions, therefore, cause the strength of the magnetic field to become very strong in some areas of the Sun. When an area of the Sun experiences a strengthening of magnetic force, where the contortedness and tangle of the magnetic field lines are at their most intense, the strength of the force reduces the amount of energy, or heat, reaching up to the surface area. As a result, the surface area is cooled and begins to appear as a dark patch rotating the Sun. This dark patch's coolness is relative to the Sun's temperature: the surface of the Sun is at 5,000 degrees; the dark patch is around 1,000 degrees cooler, therefore appearing at a dark patch, or dark spot: the Sunspot.
Just to recap: heat is generated through the smashing of elements in the core, and is transported through the radioactive and convective zones. Heat rises to the surface of the Sun, the Photosphere, and the material cools and sinks to the bottom. Strong magnetic forces, caused by the differential rotation and convective motions, cause the heat in the material of the area to subside, the area material cools, and the sunspot occurs.
Sunspots can form either individually or as part of a group. A group of Sunspots develop from a series of smaller pores with slight geographical separation, and usually accompanied by faculae. From all of the pores, one may form into a fully fledged Sunspot. The group would then consist of single sunspot and a series of smaller pores. Most sunspot groups do not evolve further than this stage; if they do, they follow a process of development described by the Zurich Classification System of Sunspot Groups describing how sunspot groups develop through a series of stages from the smallest pores through to the largest range of spots, to its decay. The exact science behind the development of sunspot groups however, is not fully understood. Continuous observations over a long period of time shall ensure the development of our knowledge of sunspot development and activity.