Functions of the to-infinitive
The to-infinitive as the subject of the sentence.
This is a formal usage and is far more common in written English than spoken:
Examples:
    To err is human, to forgive divine.
    To find fault with others is easy.
    To visit the Grand Canyon is my life-long dream.

And it is more common to say:
    It is human to err.
    It is easy to find fault with others.
    My life-long dream is to visit the Grand Canyon.

The to-infinitive to indicate the purpose or intention of an action.
In this case to has the same meaning as in order to.
Examples:
    She came to collect her pay cheque.
    I am calling to ask you about dad.
    Your sister has gone to finish her homework.

То do s.th. for somebody to do s.th. else – when we want to say that we do something so that somebody else can do something else, we can use the preposition FOR and an infinitive.
Examples:
I opened the door for them to see.

The to-infinitive to indicate what something can or will be used for. In this pattern, the to-infinitive follows a noun or pronoun.
Examples:
The children need a garden to play in.
I don’t have anything to wear.
Would you like something to drink?