Learn English – difference between “increase of ” and “increase by”

Putting aside the different grammatical constraints mentioned by @Gaston Ümlaut, there are constructions where either preposition can be used but the meaning usually differs...

...where in most cases a "call to action" is addressed to either the population at large, or everyone within some substantial community, but a "call for action" is normally addressed to government, or the leaders of some organisation (note that "a call to arms", which is far more common than either of these, is also invariably addressed to large numbers of people, not to leaders).

In most cases, a "call to action" actually seeks to persuade large numbers of people to do something "intermediate", which will put pressure on leaders to carry out the desired "action" (everyone should write to their government representative, so the government will change some policy, for example). It's fairly unusual to see the expression "call to action" used in contexts where people at large are being asked to do something that directly resolves some problem (turning down house thermostats to combat global warming, for example).

Effectively, a "call to action" asks everyone to agree action should be taken, but a "call for action" asks the relevant people to actually do it.

There has been an increase of ten per cent in the tuition fees.

The minister announced that there would be an increase of fifty cents in the tax on fuel.

There is generally a rise in the amount or number of something. An increase of X tells us the amount or percentage of the rise.