The main astrological "aspects", or angles that planets make to one another are the keys to understanding an astrological chart.
CONJUNCTION: It blends the energy of the two planets. For example a Venus/Pluto conjunction will blend the Venus energy of love, harmony, money, art and beauty with the deep, intense, secretive and possessive qualities of Pluto. This could mean the person feels love very deeply with others. It could be an intense appreciation for art and beauty, or it could manifest as being very possessive toward loved ones.
OPPOSITION: The energies are opposed to one another in some way, such as the individual swings from one quality to another but has difficulty balancing them both at the same time. For example, Neptune opposition Saturn brings the dreamy, uncertain, undefinable and idealistic qualities of Neptune together with the structured, disciplined, hard working and practical qualities of Saturn. This can mean that we can be disciplined sometimes but at others we have no plan and just "go with the flow".
TRINE: They easily combine and we are lucky with regards to the things those planets represent in our life. If our Mercury (thinking and communication) is in a trine aspect to Jupiter (luck, expansion, optimism) then we may communicate easily and often with others or we may simply think in a positive optimistic manner. Trines usually represent our personal strengths and abilities that come naturally to us.
SQUARE: The two planets are in a challenging aspect to one another. Squares can motive and energize us and compel us to great achievement, or they can simply make are life unpleasant and difficult. If Uranus is squaring Saturn for example, we may have many conflicts with our bosses and anyone in a position of power over us. If we positively handle this square aspect, we may work for innovative change within an existing power structure such as within the company we work for.
SEXTILE: There is an easy exchange between the energy of the two planets. This favorable aspect is not as strong as the Trine, but is usually beneficial. It is associated with opportunity although we may have to take the initiative to make something happen.