Here’s an idea for visualizing C operator precedence. You snake your way through the diagram starting from left to right.
Operators at the same precedence level are on the same horizontal level.
Following the arrows for changing directions, you move from left-to-right through the operators that associate left-to-right and you move right-to-left through the operators that associate right-to-left.
Although this diagram is specifically for C, many languages follow the same precedence with minor exceptions. For example, all operators that Perl shares with C follow the same precedence as C.