Need help explaining use of 'to' in a sentence

Hi there,

I'm sure this is a pretty easy answer to explain, but I need some help. I'm tutoring Chinese students online (mostly free chat and conversation), but occasionally some students have specific grammar questions.

In this case, I was reviewing a student's powerpoint. He wrote "Replying an email" and "Avoid to write long sentences."

I told him it should be "Replying to an email" and "Avoid writing long sentences." However, he had a lot of confusion over why he should and shouldn't use the "to" in each example. I couldn't offer a detailed reason why... except to say it didn't sound right! Is this a tense question? Help!