Asteroids or "minor planets" (not to be confused with "dwarf planets), are rocky or metallic bodies ranging in size from several meters to a few hundred kilometers. The term "asteroid" comes from the Greek, meaning "star-like" because that's how they appear, even in the largest optical telescopes. Most asteroids orbit the Sun between the orbits of Mars and Jupiter, in an area not surprisingly known as the asteroid belt. Other asteroids "live" elsewhere, both beyond Jupiter and even Neptune (so-called Trans-Neptunian Objects - TNO's) and among the inner planets. Those whose orbits approach or cross Earth's are designated as Near Earth Objects (NEO's). The first asteroid was discovered in 1801 by Giuseppe Piazzi and was later given the number and name (1) Ceres. Since then, more than a million asteroids have been detected. As of 2013, the Minor Planet Center, which is the official clearing house for all things asteroidal, had information on more than a million asteroids, of which more than 625,000 had enough data accumulated about them to be given a number. There are 100 times as many known asteroids as there are known comets.
Naming of Asteroids
When an asteroid is discovered, it is given a provisional designation, such as 1963 PD, reflecting the year and half month of discovery and the sequence within that half month. When an asteroid's orbit is sufficiently known to enable accurate orbital predictions well into the future, it is given a permanent designation, such as (1963) Toronto, consisting of a number and a name. The discoverer is invited to suggest a name within strict limitations (non-offensive, non-commercial, non-political, etc.). If no name has been offered or accepted after ten years, others may make an application. More about minor planet nomenclature is available at http://www.iau.org/public/themes/naming/#minorplanets .
Magnitudes
Asteroidal apparent brightness is described using the same magnitude scale as that used for stars. It is an inverse scale, meaning that the higher the number, the lower the brightness. Because asteroids vary in distance from Earth as they orbit the Sun, their apparent magnitudes change over time. Only two asteroids, (4) Vesta (magnitude 5.2 at best) and (2) Pallas (magnitude 6.5 at best) are ever bright enough to be detected without optical aid. Typically, this would be from a very dark site when they are at or near opposition (closest to Earth) and perihelion (closest to the Sun). In 2015, Vesta reaches magnitude 6.2 for a few nights either side of September 29. Pallas gets no brighter than 9.4 this year.
Observing Asteroids
Except as noted above, the observation of asteroids requires the use of a telescope or binoculars. However, no matter how high a magnification is used, asteroids always appear as mere points of light because of their small size. They can be confidently identified by observing them over time because they move relative to the background stars. By carefully noting the candidate's position, then comparing that observation with another a night or two later, such movement can be readily observed and the identity of the candidate confirmed as an asteroid. There are scores of asteroids bright enough to be detected using backyard telescopes. Over time, an observer could develop a very significant "life list" of asteroids and this activity is encouraged.
The annual RASC Observer's Handbook lists minor planets that reach magnitudes of 9.5 or brighter during the title year, giving their coordinates and magnitudes on specific dates of good visibility. Each year a particular asteroid is featured. Asteroid (15) Eunomia has the honour for 2015. Its history of discovery, physical characteristics and location in the sky are given, along with a handy finder chart. The RASC Observer's Calendar also regularly lists the dates of opposition of bright asteroids. Sky News, Sky & Telescope and Astronomy magazines (and their web sites) also routinely feature asteroids and how to find them.