Valuation rings of dim 1,2

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I am studying valuation rings (beginner). I have read some theorems but still don't know a nontrivial example. Please give me an example which is not field. Also Need help to have examples of Krull dimension 1 and 2.
Many thanks.

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As I dont know how much do you know about valuation rings and which book you are reading I can only say 2 points; waiting your response:

  • K[x] is PID (has Krull dimension 1). Localize it to the maximal ideal (x). It is a valuation ring of Krull dimension 1.
  • For a valuation ring of Krull dimension 2, see mr.bigproblem's answer to this question.