The objective is to fill a 9x9 grid so that each column, each row, and each of the nine 3x3 boxes contains the digits from 1 to 9.
When you start your puzzle, there are a few numbers already filled in for you to begin your torment.
To begin, you want to "scan". Scanning involves a couple of techniques.
First there's cross-hatching. This is the scanning of rows to identify which line in a region may contain a certain number--this is done by a process of elimination. Then do the same with the columns. You must check every digit, 1-9.
And then there's Counting. This involves counting 1-9 in the different 9-box areas, rows, and columns while looking for the missing numbers.
Advanced Sudokuers look for "contingencies" --this means narrowing a number's location within a row, column, or region to two or three areas. When those areas and numbers are within the same row, they can be used for elimination during cross-hatching and counting.