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Is there any general method by which we can find the set of all automorphisms of a group? if not then find all automorphisms of a group with the help of an example.

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    This is an old question, with many examples on MSE, e.g. [here](http://math.stackexchange.com/questions/756797/how-do-you-find-the-automorphism?rq=1). – 2017-01-01
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    It's also an extremely hard question in general. In fact, even knowing *how many* automorphisms a group has is hard. I know of one formula that works for (some!) monolithic groups (see [here](http://www.sciencedirect.com/science/article/pii/S0021869309004694)), but it obviously uses some serious machinery. If you have a specific group or family of groups in mind you can maybe get an answer, but in general, not really. – 2017-01-01
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    Even the automorphisms of the finite symmetric groups hold a surprise - for most of the symmetric groups all the automorphisms are inner, with each automorphism representing a permutation of the underlying set, but $S_6$ has an unexpected outer automorphism of order $2$. The existence of this is related to a whole host of interesting algebraic objects and phenomena. – 2017-01-01

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No, there is not a general way (it would be an immense achievement if it would be that easy) but of course there are some special cases where it is a bit easier. For example if a group is cyclic, you can work using the generators of the group. However, it is also tricky to find all of them. Some "lemmas" which may help you in the cyclic case:

  • Homomorphism are uniquely determined by their action on generators.
  • Injective homomorphisms map elements to elements of the same order (if the order of the element is finite).

You asked for an example: consider the group $(\{1\},\cdot) \leq (\mathbb{C},\cdot)$. Finding all automorphisms is easy, there is just the trivial one which maps $1$ to $1$.

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There are efficient methods for the class of finite $p$-groups, see the article

Constructing automorphism groups of $p$-groups by B. Eick, C.R. Leedham-Green and E.A. O'Brien.