How to intuitively think when developing NFA

I do not know if this question was asked correctly, but I definitely felt that it should be asked. I saw a lot of nice and informative questions, articles about internetworking, and StackOverflow itself. But I found all the questions or articles following a specific rule or template to explain the topic. I mean, when a question was asked about NFA, DFA, or regular expression, the solution was presented to the question followed by the theorems / rules of these topics (Computational Theory).

 But what I feel is that, as most of the questions on DFA/NFA are of the type 
 "Design an NFA...." or "design a DFA..." , i feel that developing/Designing DFA/NFA
 must be an ART. 

And where there is ART, I feel that there is intuition. If these problems are related to "DESIGN", then everyone should have their own path (of course, not going beyond the bounds of theorems or rules per se) solutions or attacks on these problems. To solve these problems, it is necessary to develop a thinking process (over the years of practice).

 So I would like all the experts over this Site to share their knowledge (preferably in
  simple words) how they think over the problems (simple ones) of these topics.

I would like to examine this issue in detail with a simple example.

consider the problem:

Let F be the language of all strings over {0,1} that do not contain a pair of 1s that
are separated by an odd number of symbols. Give the state diagram of a DFA with
five states that recognizes F . 

OR

Design an NFA to find a 4-state NFA for the complement of F .

(questions are taken from Sipser's book, and I also found solutions for them myself)

I just want to know how intuition can be developed to solve problems.

I ask this question, given the development of skills and the thinking process of all Beginners (like me) who encounter difficulties in solving these problems, even if they (including me) have sufficient theoretical knowledge on topics.

"" ! .

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. . . Thompson Construction. , NFA, .

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