How do you know which one is the leg or adjacent of the triangle?

There will be one angle other than the right angle that you either want to find or are given. the adjacent side is next to (touching) this angle (other than the hypotenuse). If you call the third side the opposite side, this is opposite that angle and will help you to memorise your trigonometrical ratios (SOH, TOA, CAH), whereas a leg is a leg.