Our star, the Sun, is a fairly run-of-the-mill star, plotting on the Hertzsprung-Russell Chart of star luminosity on the main sequence, along with most other stars we can see:
Hertzsprung-Russell Diagram . Observe the x and y axes, which show temperature vs. luminosity, and then find our Sun, which plots at a value of 1 for luminosity, as the basis of comparison to other stars, and rests along with most other stars on the Main Sequence line. CREDIT: NASA's Observatorium .
As you know, the Sun is a yellowish star, as shown on the diagram above. Bluer stars are hotter and redder stars are colder. Stars spend much of their lifetime with a luminosity and temperature that plots somewhere on the main sequence line. As they burn hydrogen fuel, depending on their size, they become unstable and usually become colder (more reddish) and expand in size. Hence, they are called Red Giants in later stages. Really large stars can undergo more violent changes, and can end in great explosions called supernovae. Our Sun has been burning its hydrogen fuel, fusing it to helium with a steady release of energy, for around 5 billion years. We can calculate this age on several things, but one big clue is that the Earth and Moon and pieces of rocky material (meteorites) date to as old as 4.6 billion years. There is enough hydrogen fuel in the Sun to keep it burning for billions of years to come.
NASA Solar System Chart. CREDIT: NASA's Solar System Exploration
There are nine planets in our solar system: Mecury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. The first four, Mecury, Venus, Earth, and Mars, are rocky and solid (the terrestrial planets). The rest, from Jupiter on out, are mostly gaseous (the gaseous planets). We have our Moon, but other planets have several moons, especially Jupiter and Saturn.
There is also an asteroid belt between Mars and Jupiter, at the transition point between mainly rocky and gaseous material:
Mercury Venus Earth Mars Asteroid
Jupiter Saturn Uranus Neptune "Pluto"
The Asteroid Belt occupies a position where a fully-formed planet should be, except that the huge gravitational pull of nearby Jupiter has kept the material in pieces or has broken apart an early-formed planet.
Crab Nebula M1. This image comes from the Hubble Space Telescope. It shows the Crab Nebula, a nebular cloud that seems a good fit for the beginning stages of our own solar nebula. In later stages, gravity would pull this diffuse material into a spinning disc-shaped mass of denser material, from which the planets would form. CREDIT: Hubble Space Telescope Wide Field and Planetary Camera 2 .
The Solar Nebula Hypothesis explains the origin of our solar system, some 5 billion years ago. The Universe had been around by then for near 10 billion years, so enough time had passed for stars to form in our neighborhood, have long lifetimes, and eventually die, some in dramatic supernova explosions. Gaseous interstellar material in our neighborhood, probably spread from a supernova, began to gravitationally contract, forming a disc-shaped cloud, with the protosun in the center. The sun grew hot as gravity pulled great masses of hydrogen inward, which started fusion of hydrogen into helium, and started the luminosity we still have today. Away from the center, however, cooling of material happened over hundreds of millions of years. There was more rocky material toward the inside, held in by gravitational attraction to the Sun. The terrestrial planets formed as a few larger masses (protoplanets) swept up smaller pieces within swaths of space that we now see as the orbital paths of the planets. The gaseous planets formed in a similar way, but with less rocky and dense material out there, the gaseous planets are rich in hydrogen and other gases and are large.
Earth, like the other rocky planets, underwent a transition from a soft beginning to a lifetime as a mostly solidified mass of silicate rock. Once cooling took Earth to a mostly solid state, there continued to be separation into layers and chemical reactions to differentiate material by density and chemical affinity. Today Earth retains heat, and stays hot through radioactive decay of some elements, and remains a volcanically active planet. The Moon, in contrast, is much more of a static ball. All planets underwent an early period of heavy bombardment, as pieces of solidified material was pulled in by gravity. Witness the many craters on the Moon from this period of bombardment; Earth is active, so old scars have healed over.
For a detailed version of the Hertzsprung-Russell chart, see this Wikipedia entry.
For the Solar Nebula Hypothesis, see this Wikipedia entry.
NASA has a nice Welcome to the Planets photo site.