How do they work?
The ancient Babylonians split the sky up into twelve 30 degree arcs and picked constellations that were visible within those arcs to use as references when doing astronomy and calendar stuff. That idea kicked around the ancient Mediterranean for quite a while, until the Greek version got codified by Ptolemy around 200AD, and that's more or less the version we're stuck with. So the star signs we know are the Greek version of the most visible constellations that fit into even 30 degree arcs in the night sky, as of 1800 years ago.
Your main astrological sign (sun sign, or just "sign") is which 30 degree arc the sun was in when you were born. The rest of your chart is the parts of the sky where the moon and all the planets out to Saturn were at that time. More modern charts add Uranus, Neptune, and Pluto.
Each of the signs is associated with a big enough grab bag of character traits, while the planets represent which part of your life those traits are supposed to apply to best. The exact nature of those is pretty much Calvinball though, because it's all made up and nobody is going to read Ptolemy.
The full chart is a pretty neat thing that would make for cool basis to a magic system for your next D&D campaign, though it makes me sad when people try to apply it to real life.
What about Indian astrology? Is it a branch from the original Babylonian?
So your basic idea is that the distant stars in the night sky can be divided up into constellations, and if you make even dividing lines between them, you can cyclically progress through them every year. Then, attribute personality characteristics or life patterns to the constellations. You can go ham with it and describe all the ways people associated with certain constellations will interact with people associated with different ones.
...Back so soon? You say the star sign doesn't really describe you well enough, that it's wrong more often than it's right? Well don't worry, we've got you covered. Just plot what sector the sun was in, AND what sector the moon was in. Take an extra sign or two, that way you have a way to claim personality traits from multiple star signs and distance yourself from anything that doesn't sound quite right about what you had before.
Have a sun sign, a moon sign, a rising sign, any number of signs! Just add more celestial positions to append agency to, and you'll be able to arbitrarily choose until you're satisfied with how well it "defines" you.
It's all based on your birth month/date and the position of planets on the day you were born or something idk.
Interestingly enough they should be called planet charts because there's little about stars involved.
It's also based heavily on the geocentric model of the solar system (as opposed to heliocentric), where terms like retrograde refer to the illusion of perspective that causes planets to seem to reverse direction in the night sky based on such geocentric models.
Well for one thing, if someone brings up astrology and they're only talking about the western zodiac they're probably racist