How to approach NFA design questions intuitively?
There is one sentence in your question that is worth answering:


  I just want to know , how one can develop an intuition for solving the problems?


Same thing everybody does, be is musicians, crafts men or scientists: exercise. There is no shortcut.

You can certainly use the growing database of finite-automata questions we have here. There is little use in repeating techniques here as they more often than not depend on the concrete example.

For regular languages in particular, you can devise any formal representation of the language as long as the model is equivalent to regular languages. There typically are (computable) methods to transform such representations (e.g. regular expression) to finite automata.