"By looking up, I see downward."  --Tycho Brahe 
The core belief behind astrology is that the positions and the motions of the heavens influence the lives of the people on Earth. 
The 360 degrees of the sky are broken up into thirty-six Decans of ten degrees each.  These decals are grouped in sets of three. Each set is associated with an astrological sign. The positions of the planets are mapped over this grid. 
Using a chart or computer program called Ephemeris, an astrologer charts the positions of planets, the sun and moon, and the constellations at the time of the birth of the person receiving the reading.  Once the positions have been charted, the astrologer can then calculate the relationships among them.  
The astrologer looks for several things. First off, the position of the planets and constellations are of utmost importance. Then each planet’s position is noted, with special attention paid to its relation to other planets, the House, and the horizon. Together, this information will tell the astrologer many things about the person the chart is being written for.
The angles formed by the planets are called Aspects, and they influence human relationships.  The two most powerful aspects are the Conjunction (where the planets are closest to each other) and the Opposition (where they are furthest apart). 
The Houses were originally defined in ancient Babylon.  Each of the twelve houses covers an aspect of our lives and experiences.  For example, the first house is about Life, and the second, Finance.  Each house is also associated with one of the twelve signs of the Zodiac.  When a planet appears within a house, then that planet is said to "rule" that house, and to influence that aspect of the person's life. 
Charts can be drawn for both people and events.