How can you test astrology to see if it's right or wrong?

Short answer: Statistics.

Longer answer: First of all, there is no particular reason to believe it's right. Why would being born on a certain date affect your character, for example, or any of the other implausible claims made by astrologers? What mechanism would affect your character, for example, or your luck?To actually test some of the claims, you could apply statistics. Given the popularity of Astrology, I am pretty sure that several such tests have already been made. If you want to test it yourself, you could check some of the predictions of astrology. Be aware that many of the predictions are intentionally vague; be careful about those. You would need to find predictions that are actually verifiable, and compare results (for example) for several people born in a certain sign (assuming the prediction says something about what will happen to people of that sign), to people who are not of that sign. Note that a single confirmation doesn't really prove anything; you need a larger sample. Check statistics textbooks, to see how large your sample should be, to be considered "statistically significant".

But you may first just want to search the internet, to see whether other people already went through all this trouble.