The first thing to know and remember is that nothing in your or any chart is good or bad. Astrology is about energy and time, and our attitudes and levels of openness determine how we will experience the energies and times.  For example, in traditional astrology's treatments of aspects, we often hear that squares are bad and trines are good.  The nature of a square is to apply pressure and it can be difficult for a person when that pressure comes on, but there's an opportunity to incorporate something new or forgotten with the square - so if you're open to the idea of a little work (after which you're likely to be better off), squares can be terrific.  Trines, then, are supportive in nature and thought therefore to be good, but we may find that when things get easier we lose our motivation.  This applies to everything in astrology - planets, transits, aspect configurations - everything - nothing is automatically good and nothing is automatically bad.

Given that astrology's a language, it can be helpful to break it down into its elements to get a sense of what's what. The basic three elements:

Planets
Note: The Sun and Moon are considered planets in astrology.
Planets represent drives, or energies - a what.

Signs
Signs represent styles; ways we approach things - a how.

Houses
Houses represent arenas of life - the where.

While each of us has Mars in the birth chart, everyone's Mars placement will be different. A worthwhile analysis of your Mars will look at everything affecting Mars in your chart: What it is (the drive to initiate), how it's going to go about doing what it does (its sign), what arena of life it will play itself out (its house), and what aspects it makes to other planets (how it's tied in to the person's other energies - see below for a note on aspects).

Nodes of the Moon/Nodal Axis
The Moon's nodes are the points where its orbit around the earth crosses the earth's orbit around the Sun. So, they're not planets or any kind of bodies at all, but are extremely important in chart analysis. Evolutionary astrology uses the Nodes and Pluto to evaluate the karmic issues which are in this life at the forefront. Very broadly, the South Node represents past life issues, and the North Node represents the direction we are in a way pointed in this life in order to grow.

The South Node, as the past, indicates something we're comfortable with and, if pursued, might be a way to have success in the world. Sounds good, right? There's a catch: We won't be happy if we pursue only the activities and arena of life represented by the South Node. The North Node represents something we're probably not so good at without effort, and it's where the soul wants us to head in this life - we haven't done this as much as we've done what's represented by the South Node. A healthy strategy is one of integration, wherein we take what we know from the South Node and apply it in the opposite direction, the North Node.
The rest of the chart, then, is indicative of the personality the soul has chosen to play out/work on those karmic issues.

Angles
There are four points also to consider in a chart, angles. They're the ends of two axes, each of which divides the chart wheel into halves. The Horizon's poles are the Ascendant and the Descendant, and the Meridian's poles are the Midheaven (MC) and the Nadir (IC). The signs these poles are in indicate something about how we approach the houses of which they mark the beginning:

Ascendant    The beginning of the 1st house, the house of personality and body - also called the Rising sign.
Descendant  The beginning of the 7th house, the house of others.
Midheaven    The beginning of the 10th house, the house of our role in the world.
Nadir            The beginning of the 4th house, the house of our role in our family or home and self.

Aspects
Aspects are the relationships formed by planets in the chart wheel. In a natal chart, they're typically indicated by colored lines between planets, and using them to tie together the planetary placements can make the natal chart come alive.

There are major and minor aspects, the major aspects being based on 30-degree increments of the wheel.

The major aspects are the conjunction (0 degrees), sextile (60 degrees), square (90 degrees), trine (120 degrees), opposition (180 degrees) and quincunx (150 degrees, also called inconjunct). Minor aspects divide the wheel in different ways, and are not as much in use - good and useful work can be and is done without them.

All aspects are considered using what's called the orb of aspect (generally just called "the orb"). It's the leeway we give the angular relationships between planets: two planets 93 degrees from each other in the wheel can be in square, as well as two planets 85 degrees from each other in the wheel. The closer to 90 degrees from each other they are the more important the square (the greater effect we should expect from it), and astrologers vary in their opinions as to how wide orbs should be.

Transits
Transits are the movements of the planets. Your natal (birth) chart is the map of the sky, from the perspective of the earth, at the moment you were born. After you were born, however, the planets continued to move. Looking at transits means looking at the planets' current movements in the sky in relation to their placements in your natal chart.

Progressions
Secondary progressions are a theoretical approach to long-term psychological growth. Your natal planets are moved forward one day for every year of your life (so, if we want to look at your progressed chart at age 34, we look to where the planets were on the 35th day following your birth - because at 34 you're in your 35th year of life). The summary idea is that you are a set of potentials which is a moment in the history of the universe, and looking at progressions after the natal and transit charts can help illustrate some big-picture stuff about how you-as-that-moment unfold over the course of your life.