The Basics

Firstly, it's impossible to get very far without carefully maintaining a list of 'possible values' or candidates for each blank cell. Systematically analyse at each blank cell. Start with the assumption it can have any digit (or value) between 1 and 9, and then remove all values which have already been assigned to other cells in its respective row, column and 3x3 box. This leaves each blank cell with a list of candidates. Repeat the following logical steps until the puzzle is solved. Only progress to more difficult steps when simpler steps neither reveal new values nor exclude candidates from blank cells.

Singles

Any cells which have only one candidate can safely be assigned that value. It is very important whenever a value is assigned to a cell, that this value is also excluded as a candidate from all other blank cells sharing the same row, column and box.

Hidden Singles

Very frequently, there is only one candidate for a given row, column or box, but it is hidden among other candidates.


Beyond the Basics

While the two steps above are the only ones which will directly assign a cell value, they will only solve the simplest puzzles. That's fortunate, otherwise Sudoku wouldn't be as popular as it is today. The following steps (in increasing complexity) will reduce the number of candidates in blank cells so, sooner or later, a 'single' candidate or 'hidden single' candidate will appear.

Locked Candidates 1

Sometimes a candidate within a box is restricted to one row or column. Since one of these cells must contain that specific candidate, the candidate can safely be excluded from the remaining cells in that row or column outside of the box.

Locked Candidates 2

Sometimes a candidate within a row or column is restricted to one box. Since one of these cells must contain that specific candidate, the candidate can safely be excluded from the remaining cells in the box.

Naked Pairs

If two cells in a group contain an identical pair of candidates and only those two candidates, then no other cells in that group could be those values. These 2 candidates can be excluded from other cells in the group.


Advanced Steps

Naked Triples & Naked Quads

The same principle that applies to Naked Pairs applies to Naked Triples & Naked Quads.
A Naked Triple occurs when three cells in a group contain no candidates other that the same three candidates. The cells which make up a Naked Triple don't have to contain every candidate of the triple. If these candidates are found in other cells in the group they can be excluded.

A Naked Quad occurs when four cells in a group contain no candidates other that the same four candidates.

Hidden Pairs

If two cells in a group contain a pair of candidates (hidden amongst other candidates) that are not found in any other cells in that group, then other candidates in those two cells can be excluded safely. Hidden triples are generally extremely hard to spot but fortunately they're rarely required to solve a puzzle.

Hidden Quads

If four candidates are restricted to four cells in a given group, then all other candidates in those four cells can be excluded. Hidden Quads are very rare, which is fortunate since they're almost impossible to spot even when you know they're there.

So now get started on your first Sudoku puzzle here.