The most basic component of any chart are the elements -- fire, earth, air and water. When taking a first look at a chart, take a look at the elements in play. That's one of the first things I'll do, when I've got a new chart in front of me. Along with that, the graph at the bottom will usually show you the elemental make-up of a chart.
For example, you might see that there's a major emphasis on earth in a chart. Perhaps there's even a grand trine, with planets in each of the earth signs. That's a biggie, and can be considered a gift, or harmonious flow of energy, in the chart. Or you see that two elements are dominant. This will become an important anchoring theme for your overall interpretation of the chart.
A Real Life Example: Recently, I read a chart for a Pisces Sun (water), with most of the other planets in fire signs (Aries and Sagittarius). The elements help you understand a person's basic temperament. It explains why this Pisces comes across as very fiery. It makes him a more strong-willed Pisces, less likely to flounder without direction. The sensitivity is still there, though, and that has to be taken into account for his well-being. Water and fire make steam, and this is evident in this musicians on-stage persona.
The elements in a chart can seem at odds with each other. In those cases, a life lesson is learning to harmonize seemingly discordant energies. Not easy! An example is harmonizing an air emphasis (intellect, detachment) with a heavy water emphasis (emotion, union, imagination). Some with these elements have to work at getting out of the head, to be able to feel a heart connection with others.
Looking at the elements in the birth chart, is a great place to start. Take what you've learned from the chart, and see how it fits with your observations. If it's your own chart, you might find it illuminating to see that just beyond your Sun in Cancer, is a slew of planets in Virgo. Since you are a blend of energies, knowing the elements of all the planets gives you the energetic big picture.