Astrology can be a very complex science. There are many aspects to consider when determining compatibility between two signs. One of the best, easiest, and often overlooked way to see if two signs are compatible is by simply understanding the elements.
There are four elements, and each one is attributed to three specific signs.
Fire
Aries, Leo, Sagittarius
Air
Gemini, Libra, Aquarius
Earth
Taurus, Virgo, Capricorn
Water
Cancer, Scorpio, Pisces
Each of these elements have certain characteristics, and I will give you a brief summary of what those are.
Fire
Positive, Assertive, Determined, Active
Air
Social, Intelligent, Doers, Communicators
Earth
Stable, Enduring, Structured, Introverted
Water
Passive, Receptive, Reactive, Intuitive
It could be possible that you are beginning to understand which elements are the most likely to blend well together. As a "general" rule, in dealing with the elements, Fire mixes with Air, and Earth mixes with Water. I know it seems far too general, and much too simple to be taken seriously, but in my experience it can create a solid foundation in considering compatibility. If you are a casual Astrology fan, and calculating planetary aspects between two charts is not your bag, then this is a much simpler formula you can incorporate. You will find that it sells itself in the end. You can also get insights as to why you are most attracted to certain types of people, when the "general" rule does not seem to apply to you specifically. Of course, a natal chart would most definitely complement this, because you would be able to see exactly why you find yourself leaning towards a certain type. There is a great number of free sites that you can find on the web that will generate a natal chart for you. For instance, my personal natal chart does not contain a single Earth, or Water element sign. I often find myself very drawn to the Earthy signs, and Alpha personalities. But, on the other hand, very distant from Water signs. This is because I am predominately Air influenced. Air, and Water signs have the most trouble blending together. Those relationships can be difficult if there is not some sort of balance elsewhere in the horoscope. Which is a good start at better understanding who your attracted to and why. Chinese Zodiac Signs are also element influenced.