How do I know if I need to pay taxes on my day trading income?

You need to speak with a CPA (Certified Public Accountant) or similar professional in your own country/jurisdiction in order to receive advice on the tax laws and requirements you must follow when you earn income from trading in the stock market.  If you are in the U.S. you can watch this webinar with Robert Green from GreenTraderTax.com where he does a presentation and and answer session regarding various tax related elements, especially the Trader Tax Status (TTS) as well as many questions posed by our members https://bearbulltraders.com/course/technology/lesson/brokers-commissions/topic/green-trader-tax-webinar/