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Each row, column, and nonet contains each number exactly once. The sum of all numbers in a cage must match the small number printed in its corner. No number appears more than once in a cage. (This is the standard rule for killer sudokus, and implies that no cage can include more than 9 cells.)
When one hears that no math is required to solve Sudoku, what is really meant is that no arithmetic is required. The puzzle does not depend on the fact that the nine placeholders used are the digits from 1 to 9. Any nine symbols would serve just as well to create and solve the puzzles.
In general, to use the 45 rule, look for a row, column or block where all cages except one lie completely inside. For an inside square, the solution is always 45 the inside total. For an outside square, the solution is always the outside total 45.
To solve a Sudoku puzzle, one needs to use a combination of logic and trial-and-error. More math is involved behind the scenes: combinatorics used in counting valid Sudoku grids, group theory used to describe ideas of when two grids are equivalent, and computational complexity with regards to solving Sudokus.
The most basic strategy to solve a Sudoku puzzle is to first write down, in each empty cell, all possible entries that will not contradict the One Rule with respect to the given cells. If a cell ends up having only one possible entry, it is a forced entry that you should fill in.