Among those verbs:
Preguntar is the verb used most commonly to mean "to ask a question" or "to ask about" something. It is often followed by the preposition por to indicate the subject of the inquiry:
- Preguntó por la situación legal de su hermano. He asked about his brother's legal situation.
- Pablo preguntaba por ti. Pablo was asking about you.
- Pregunté si había estudiado la lección. I asked if she had studied the lesson.
Pedir is usually used to indicate a direct request or to ask for (rather than about) something. It does not have to be followed by a preposition.
- Pidió un coche azul. She asked for a blue car.
- Sólo pedí que repararan el techo. I only asked that they repair the roof.
- ¿Te pidió dinero? Did she ask you for money?
Rogar can mean to formally ask or to make a formal request. And depending on the context, it can also mean to beg or to pray.
- Le rogamos que indique los números de teléfono completos. We request that you indicate the complete telephone number.
- Se ruegan los clientes que tomen las precauciones oportunas para salvaguardar sus pertenencias. Customers are asked to take appropriate precautions in order to protect their belongings.
- Te ruego que tengas piedad con mi madre. I beg you to have pity on my mother.
- Fueron a la iglesia para rogar. They went to the church to pray.
Invitar can be used when asking someone to do something or go somewhere, much like the English cognate "invite."
- Nunca he invitado a nadie a postear en mi blog. I never have asked anyone to post on my blog.
- Te invito a mi casa. I am asking you to my house.
- Solicitan amnistía para ex presidente. They are asking for amnesty for the former president.
- Solicitaron sus opiniones profesionales sobre el proyecto. They are asking for his professional opinions about the project.
