For starters - I wash all my washable fabrics before cutting them so there is little or no shrinkage when pressing the pieces or units.
Then I make sure that my pieces are the right size to fit together properly. Occasionally there is an error in the directions or the template. (How do I know this!)
I usually nest the seams. For units with sharp angles in them like the triangle in a square - I mark the pieces where the "points" are and match those points. And pin. I don't pin a lot.
I am working on a piece where many many seams come together - the seams are pressed open - I have resorted to hand basting to reduce slippage. There is still some slippage - and I'm living with it - but it does help.