The 5 planets known to the ancients (Mercury, Venus, Mars, Jupiter and Saturn) can be the next brightest objects in the sky after the sun and the moon. All the planets (except pluto) have orbits which are more or less in the same plane as the Earths orbit around the Sun - see this java animation (click and drag the mouse to get the solar system edge on). So their positions projected onto the sky again project onto the same constellations as the suns motion around the sky - so the planets are also seen only along the ecliptic, projected against the zodiacal constellations. All the planets revolve around the sun in the same direction (anti-clockwise as seen from above the north pole of the Earth). These 2 facts (same plane and direction of rotation) are important for theories of how planets form. They are consistent with ideas of a disk of material rotating around the young Sun which then condenses into planets.
Understanding orbital motion is a key to understanding the motions of the solar system. Gravity is stronger nearer the sun. Planets that are closer to the sun then need to have higher speeds in order to balance the higher pull of gravity. But they are also closer in so the distance they have to travel is shorter. The time for the inner planets to make 1 orbit is then a lot shorter than for the outer planets. Mercury's orbit is at a distance from the Sun which is only 0.39x that of the Earth's, so if it had the same orbital speed it would have a 'year' which is 0.39x that of the Earths also. But in fact the the 'year' for Mercury is 87.9 days, only 0.25x that of the Earth, because its orbital velocity is bigger to compensate for the higher gravitational pull. So it has a shorter distance to go around AND a higher speed, so its orbital period is much shorter. For the outer planets they have further to go and a slower speed so their orbital periods are much longer than that of the earth. e.g. saturn is 9.5x further from the sun than the earth is, but its orbital period is 29.5x that of the earth.
Planets shine in visible light only by reflected sunlight. So they can show phases. The inner (or inferior) planets show the full range of phases, and they can never be very far from the sun in the sky. More on phases of Venus (Mercury is similar). Inferior conjunction is earth-planet-sun. Superior conjunction is Earth-Sun-planet. Maximum Eastern elogation is when the inner planet is visible in the western sky as an evening star (its east of the Sun). Maximum Western elongation is when its visible in the eastern sky as a morning star. Here is a nice diagram.
For the outer (or superior) planets then conjunction is Earth-sun-planet (planet furthest from Earth) and opposition is Sun-Earth-planet (planet closest to Earth (see the previous diagram. They can also show phases but only from full to gibbous - they can never be new or crescent as they can never be between the Earth and the Sun. More on aspects and phases of the planets
Because the outer planets move more slowly than the Earth then the Earth can catch them up and overtake them! So from the Earth we see them going backwards. This is called retrograde motion, and was one of the puzzles of ancient astronomy. This happens at opposition (sun-Earth-planet). More on planet motions and retrograde motion
The time for a planet to be back in the same position with respect to the earth eg the time between sucessive oppositions is NOT the same as the planets orbital period. The earth is not just sitting here while the planet moves around - its also rotating anticlockwise around the sun. So the time taken for the planet to get back to where it started from with respect to the sun and earth (synodic period) is LONGER. Time to get back to relative positions: Fast moving object gets back to where it started in time P1 (its orbital period), but the slower object has moved on a bit. Let S be the synodic period, where the fast object has gone through an angle of 360+theta. So (360+theta)/360=S/P1. But the slow object has gone through an angle theta in this time so theta/360=S/P2. So substitute for theta/360 to solve for S and get 1/S=1/P1 - 1/P2. So for the Earth (slow P2=365.25) and Venus (fast P1=224.7) we get 583.9 days. There is exactly the same effect on the Moon - the Moons orbit is 27.3 days with respect to the stars but the Earth moves on a bit so the synodic period for the Moon ie time between sucessive full moons is 29.5 days.
The brightness of a planet then depends on how much sunlight they intercept (distance from sun and size of planet), how much they reflect (composition - clouds reflect more light than rock!), how much of this can be seen from Earth (phase) and distance from Earth. Outer planets are brightest at opposition (closest Earth-planet distance and full phase). Inner planets are more complex because at their closest distance they are at minimum phase.
The inner planets (mercury, venus, earth and mars) are small and rocky while the outer planets (jupiter, saturn, uranus and neptune) large and much less dense - gas giants. Pluto is a bit of an anomoly. See relative sizes