One easy way to determine that astrology is unscientific is this: It's so-called predictions can't be tested, which is one of the standard components of the scientific method. Instead, horoscopes are carefully worded to be highly general, such as "You will face great difficulties ahead." Any result, from getting fired from your job to getting a raise, could be seen as fitting those expectations.
Still, horoscopes remain popular, something psychologists think is at least partially a result of the fact that we're biased to see "personalized" results as accurate. This is called the Forer Effect after psychologist Bertram Forer. In 1948, Forer gave each of his students a personality test and then told them that each "result" was individually unique. He asked them to rank the tests' accuracy and on average, they said it was 85% accurate. Later, he revealed to the students that he'd lied and given them all the exact same result.