We use "para" after the verb ir when we want to talk about a direction or destination. "Eu vou para sua casa amanhã" "Você vai para o Rio de Janeiro?" "Como você foi para a festa ontem?" But, in informal portuguese, it will be something like: "Eu vou pra sua casa amanhã." "Você vai pro Rio de Janeiro?" "Como você foi pra festa ontem?" In these phrases you said, the first one is extremaly formal. You will read it in few books. Eu vou ao supermercado. -> "Eu vou para o supermercado" or even "Eu vou pro supermercado". The last one more common. Eu vou para falar com o professor. -> this one just like an answer, like: "Por que você vai para escola hoje?" "Eu vou para falar com o professor" I hope I was able to help you! Any question you can ask me :)

Well, u can use: 'Ele pediu para ir ao médico com ela' in english 'He asked to go to the doctor with her'. In this case 'para' as a preposition followed by the infinitive verb form 'ir'. You've used correctly when u said "Eu vou ao supermercado'. But on your second example the sentence is correct only if u were intending to say that your purpose was going somewhere exclusively to talk to the professor, like when u have this dialogue: Question - "Why are u going to college today?" Answer - "I'm going in order to talk to the professor.

Adding to the previous answers, "ao" and "à" can basically mean "to the", with "ao" being used before male nouns and "à" before female nouns. For example, it is correct to say this, because supermercado is a male noun: Eu vou ao supermercado. But you would say this if you used the word "loja" instead, a female noun: Eu vou à loja. Also, by making the noun indefinite, you drop the o and the ` entirely: Eu vou a um supermercado. Eu vou a uma loja.