Aaron Marino of alpha m. says that when wearing a shirt you can untuck, tuck, and partial tuck. Untucked shirts are best when casual: tee shirts (long and short), Henleys, sweaters, and proper length button-downs. Fully tucked is best with dress shirts or dressed-up tee shirts with sport coats.
If you're going kind of casual cool, and you don't want to tuck your shirt but you have a sweet-ass belt on. A perfect option is the partial tuck. It needs to look like it happened by accident. Alpha demonstrates how to do it: gently lift shirt and place a little bit of it in where one of the belt loops are. Have it fold under and let it drape. You don't want it tucked all the way around. If your shirt is super long, it'll look funny.
Avoid the partial tuck of the button-up dress shirt. You can partially tuck light-weight sweaters. You need the proper length for the shirt, and you don't want to go super symmetrical (angle at belt loops). Gently fold to mid-point.