Short answer: Cut vegetables evenly, dry them well, preheat the pan, cook a manageable amount, and add ingredients according to how long they need. Sauce should go in near the end.
Water on the vegetables and an overcrowded pan create steam. Dense stems may need a head start, while leafy parts cook last. If your burner is modest, cook in batches and combine everything briefly with the sauce. Crisp does not mean raw: learn the desired texture for the specific vegetable.