When playing hitori I have found that the best way to proceed is to look for and spot patterns that help you solve the puzzle.
Make a note of these puzzles as you go along and you can solve almost any puzzle quickly. I reckon I have noted down about ten patterns, several of which will appear in any one puzzle, that you can use to work through to the solution for that puzzle.
One of the easiest is if you have the same number three times in a row, for instance.
Here you know that the middle one must be left white, and the two surrounding it marked black or filled.
Because otherwise if the middle one were filled, then the two other one's would both have to be white, but this is not possible.
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