“Approach to” or “approach for”

Question:

When do you use approach for, and when do you use approach to?

(How can I answer questions like this? In which dictionaries should I look? How do I google it?)

Answer:

When used as a verb, 'approach' takes no preposition. However, when as a noun, it requires a preposition, otherwise you end up with two nouns in a row: "The pilot's approach [ ] the runway was too low." The question is which preposition is most appropriate.

Using the more literal example I gave above, it's easy to see why 'to' is more appropriate than 'for', and this still holds for more abstract uses:

"my approach to the problem"

"an iterative approach to the travelling salesman problem"