Samurai sudoku puzzles follow the rules of traditional sudoku. All you need to do is get your head wrapped around them the right way.
Think of them as five overlapping 9x9 grids. Every row, column, and 3x3 cage of these individual grids must contain one and only one example of the digits from 1 to 9. That's just like a regular sudoku.
Of course what makes it tricky, but also what is a source of clues, is that the four overlapping cages must serve two puzzles at a time. There is, of course, only one solution. So don't guess, deduce!
If you are new to this game, go ahead and print one out and get started. You'll catch right on and soon be an expert!