To make a plasma, you need to have something to confine it in. The sun keeps together the hot plasma by gravity, which causes a very high pressure in the center of the sun. In order for gravity confinement to work, you have to make the plasma big, very big, like the sun. On earth such conditions cannot be reproduced, so a different technique needs to be used. And in contrast with what you may think, the sun "burns" quite slowly. A cubic meter of the center of the sun only produces 30 watt, barely enough to power a light bulb.
Although many different fusion reactions are possible, only a few of them are interesting for fusion power production on earth. Those are the reactions that are possible at a relatively low temperature, for fusion standards anyway. The fusion reaction that is currently considered to be most suitable for energy production on earth is the reaction between deuterium and tritium. Deuterium is a stable isotope of hydrogen, with one extra neutron in its nucleus, tritium is an unstable isotope of hydrogen, and has two extra neutrons.
To produce enough fusion reactions for useful power production, the deuterium-tritium mixture has to be brought to a temperature of 150 million degrees; ten times the temperature of the center of the sun! Of course, no single material can withstand such temperatures. Somehow, the plasma must be kept away from the walls of the plasma vessel, because if the plasma does touch the wall, the wall would get hot and the plasma would get cold, and, fusion would stop. The plasma must be contained.
To accomplish this, we can use a property of the plasma: as it consists of charged particles - positive nuclei and negative electrons - a plasma can be influenced by a magnetic field. It is a property of charged particles that they follow magnetic field lines. The magnetic field lines can be organized in such a way that the plasma does not touch the inner wall of a plasma vessel: this technique is called magnetic confinement. In modern fusion experiments, the plasma is confined in a doughnut-shaped vessel with magnetic coils called a tokamak.
This doughnut-shaped vessel, also called a "torus", must be in vacuum before the deuterium and tritium fuels are injected. The fuel then has to be heated (with a variety of heating methods) so that it becomes a plasma. Using superconducting coils (blue in the illustration) a magnetic field is generated, which causes the plasma particles to run around in circles, without touching the vessel wall. In reality, a number of other coils are present, that produce subtle changes to the magnetic field, intended to stabilize the plasma.
Read more about the ITER reactor.