Verbals

Gerunds and infinitives are called verbals.  They are verb forms that function as nouns (in most cases).  A gerund is the -ING form of a verb without an auxiliary:  eating, studying, working, etc.  An infinitive is TO followed by the simple form of a verb:  to eat, to study, to work.

Both gerunds and infinitives can function as subjects, but gerunds are more common (infinitives are very formal):

        1.  Eating is a great pleasure.
        2.  To eat well is an art.

Both can function as objects of verbs.  This is the great problem in using gerunds and infinitives because some verbs are followed by a gerund, some by an infinitive, and some can be followed by either:

        3.  I want to take a vacation.  (must be an infinitive)
        4.  She enjoys working.  (must be a gerund)
        5.  She likes to work.  (gerund or infinitive)
        6.  She likes working.  (gerund or infinitive)

        7.  *I want taking a vacation.  (must be an infinitive)
        8.  *I enjoy to work.  (must be a gerund))

Only gerunds can be the object of a preposition:

        9.  She is thinking about eating.

Usually infinitives are the verbal complement of an adjective:

        10. She is eager to work.
 

The links below will give more complete explanations and a number of exercises.

Links:

        Explanation and exercises on gerunds only:  gerund.htm
        Gerunds and infinitives:  gerinf.htm
        More advanced explanation:  gerunds.htm
        Another exercise:  exercises/fitterqz.htm
        One more exercise:  GERUNINF/Gramb.htm