For coins, simply slice off rounds by cutting the carrot crosswise. You want to aim for evenly sized pieces so they cook at the same rate, so reduce the thickness of your slices as they increase in diameter.
Slabs are just bigger coins. Same idea, except place your knife at a sharp angle (almost parallel) before slicing down.
For sticks, cut the carrot in half lengthwise, then halve again. If your carrot is big, you may want to cut it into thirds. Then cut those pieces crosswise into shorter sticks.
Dice carrots by simply gathering sticks into a row and slicing crosswise into small pieces. They won’t be perfectly square, but square enough.