This is a jukugo word, which usually means on'yomi readings from the kanji. Counting days, however, are an exception (at least up to ten). You need to use the kun'yomi readings to read this word. You already know the kun'yomi reading for 三 from when you learned the word 三つ. Here is a way to remember the reading for 日:
On the third day you have to give me (み) a ride in your car (か). I don't have a car of my own, so don't forget me, okay?
Where did those two people meet on the third, two months ago?
I haven't had water for three days.
The third day of March is Girl’s Day.