I have my synastry chart! Help me read it?

Your chart doesn't show the Ascendants. Nor does it show the degrees that the planets are in ...
The aspects are what show HOW you two get along (or not), and aspects are distances that are measured in degrees.

In order for a relationship to be serious and long-lasting, you need to have one person's Ascendant or Descendant within 8 degrees (conjunct aspect) of the other person's Sun or Moon or Venus or Mars. Or the other way around.

Without this, good aspects make for a pleasant short-term affair.
With this, if there are many bad aspects and the two people don't learn to overcome these challenges, even the stronger Asc/Desc. contact will not survive 10-15 years together.

I'm about off to bed, but I'll help you help yourself.
Site #1 will give you a list of aspects between your two charts. Look for those Asc./Desc. aspects listed above. Also write down the aspects this site gives you:
http://www.configurationhunter.com/astrology-online/free-synastry.php?zi=26&luna=6&an=2012&ora=02&minut=18&timezone=HAST&zi1=26&luna1=6&an1=2012&ora1=02&minut1=18&timezone1=HAST&conjunction_orb=8&sextile_orb=6&square_orb=8&trine_orb=8&opposition_orb=8&customangle=1&customorb=0&aspecttype=AL&sun=1&moon=1&mercury=1&venus=1&mars=1&jupiter=1&saturn=1&uranus=1&neptune=1&pluto=1&northnode=1&sun1=1&moon1=1&mercury1=1&venus1=1&mars1=1&jupiter1=1&saturn1=1&uranus1=1&neptune1=1&pluto1=1&northnode1=1

then go to site #2 and use their "score sheet" approach for determining the aspects, to see whether the comparison is stronger on the positive or negative side:
http://cafeastrology.com/synastry.html

Synastry charts show the good, the bad, and everything else in between. It can be confusing when you don't know how to put the small details ( like house overlay or an aspect ) and apply it to the whole of the chart. You can have a heavy Moon-Pluto square in the chart, but have a Venus-trine Mars, Moon-Jupiter trine, and a Venus-Jupiter sextile, as well as a Jupiter-Pluto trine to help smooth things over. House overlays are also neat. Id say read the chart like how you read a natal chart. Some aspects are stronger than others. If a bunch of planets fall in a particular house, then there is likely to be an emphasis on it.