Questions about to in English: When does it mean to do and when does it mean to doing? Please explain in detail.

The to in to do is an infinitive symbol, indicating that the verb following it can no longer be used as a predicate. To do is called the infinitive form of a non-predicate verb and can be used as a subject, object, object complement, Slogan, attributive, adverbial:

1. (To see) is (to believe). Seeing is believing (as subject and object, if you use see, believe is wrong, because believe see is a predicate)

2. He left, leaving me to do all the rest work. had no place to live. He had no place to live. (Attributive)

4. To be fast, I speed up. To be fast, I speed up. (Adverbial)

Non-predicate There are many complicated uses of verbs. It is recommended that you study it carefully in a grammar book.

To in "to doing" is a preposition, followed by a noun or gerund.

Generally, to do and to Doing depends on your daily accumulation. Remember some fixed collocations to see if they are prepositions or infinitives.