-ing forms and infinitives

Prepositions are not normally used before infinitives in English. After verb/noun/adjective + preposition, we usually use the -ing form of a following verb.

• He insisted on being paid at once. (not He insisted on to be paid …)
• I don’t like the idea of getting married. (not … the idea of to get married.)
• I’m not very good at cooking. (not … good at to cook.)

In some cases we drop the preposition and use an infinitive. Compare:

• He asked for a loan.
  He asked to borrow some money.
• She was surprised at his mistake.
  She was surprised to see what he had done.
• We’re travelling for pleasure.
  We’re travelling to enjoy ourselves.

Sometimes two structures are possible. There may be a difference of meaning (see here) for some examples).

• I’m interested in learning more about my family.
• I was interested to learn that my grandfather was Jewish.

note

For details of the structures that are possible after a particular verb, noun or adjective, see a good dictionary.