Ask: preguntar
Ask sin más es preguntar: Can I ask you something?, She asked me my name. Recuerda que hacer una pregunta es ask a question, no make a question.
Ask for: pedir algo
Para pedir una cosa, ask for: I asked for the bill, He asked for help. Sin for, ask significaría preguntar.
Ask someone to: pedir que alguien haga algo
Pedirle a alguien que haga algo es ask someone to: She asked me to wait, I asked him to call me. Nunca She asked me that I wait.
Order: en el restaurante
Pedir comida o bebida es order: Are you ready to order?, I ordered a pizza. También para compras por internet: I ordered it online.