SudokuPower is your online sudoku resource.
If you are stuck, click the hint button to reveal the available hints & then select a hint. The site will now highlight the hint. The darkblue colored cells are affected by the the pattern found in the lightblue colored cells.
You can apply the result of the hint by doubleclicking the selected hint. Please keep in mind that if you are using hints, the hall-of-fame will not be updated after solving the puzzle.
The following types of hints are available.
When the site hints for a naked single, this means there is only one possible number in a certain cell, for example: 
If you analyze the light-blue coloured cells, you will see that the numbers 1,2,3,4,5,6,7 & 9 are already there. So the only value left for Cell 1,4 is an 8.
When the site hints for a Hidden Single, this means there is only one remaining location for a number in a unit (row, column or 3-by-3 box). For example: 
When you analyze the highlighted cells you will draw the following conclusions:
1. There are only 4 positions left to place a number.
2. You cannot place a 1 in cell 2,1. (The 1 is already present in the row in cell 6,1)
3. You cannot place a 1 in cell 2,2. (The 1 is already present in the row in cell 9,2)
4. You cannot place a 1 in cell 2,9. (The 1 is already present in the 3-by-3 box in cell 8,2)
So the only place left to fill in the 1 is cell 2,3.
A lot of hints will only allow you to eliminate candidates for cells. Before you can start eliminating candidates per cell, you have to fill all cells with remaining candidates.
So when you have has run out of naked singles and hidden singles, the site will hint you for filling in the candidates: 
All you have to do now is fill in all remaining candidates for every cell.
For example: In the upper left cell, you can only fill 1,2,4 & 7, because all other numbers conflict with already found numbers in the row, column or 3-by-3 box the cell is part of. So fill in those candidates in that cell.
Once you've started filling the cells, you will probably start noticing all kinds of patterns which will help you solve the puzzle.
This hint means that a cell has too many candidates: One ore more candidates aren't possible if you apply the basic Sudoku constraints. For example:
In this case cell 6,4 (The dark blue coloured cell) is affected by the light blue coloured cells (Every number can only occur once a box, row and colomn).When you analyze the light blue cells, you will notice a filled number 7 in cell 6,5. Hence you can eliminate the number 7 as a candidate in cell 6,4.
5: Intersection I: digit in box must be in row or column
This hint means that in a row or column the only remaining candidates intersect with a 3-by-3 box. In this case you can eliminate all other candidates in that box. For example: 
If you analyze this pattern, you will see that the only remaining 9's in Column 8 are all in the upper 3-by-3 box. Therefore you can eliminate the number 9 in the other columns in that box.
Explanation: if you would place a 9 in one of the darkblue cells this would eliminate all remaining 9's in Column 8, violating the sudoku constraint that each column must contain all numbers.
6: Intersection II: Numbers lined up in box
Although you may not yet know the exact location if a number in a box, you still might know in which row or column the number will be placed. In this case you can eleminate all other candidates of that number on the found row or column. For example:
If you analyze the candidates in the lower left box, you will see that the remaining candidates of number 1 are all in the top row of the lower left box. This means that although you do not know the exact location of the number 1 in the box, you do know that number 1 will be placed in the top row of that box. Therefore you can eleminate all other 1's in that same row (in this case: The number 1 in Cell 6,7)
Explanation: Placing the 1 in Cell 6,7 would eliminate alle 1s in the lower left 3-by-3 box, violating the constraint that all boxes must contain all numbers.
7. Naked Double, Triple, Quad & Quint
This type of hint is know a naked set. A set of cells is a naked set when in a unit (row, column of 3-by-3 box) there are N cells which contain only N remaining candidates. In that particular case you can remove the candidates for all other positions within that unit.
As you can in this example, in row 6 there are 2 cells (positions 2 & 8 in the row) which contain only a 1 and a 5. In this case you can remove these numbers from all other cells. (the 1 and 5 on positions 6&9).
8. Hidden Doubles, Triples, Quads & Quints
This type of hint is known as a hidden set, which is basically the opposite of a naked set (see previous hint): N candidates are only possible on N positions, in which case you can eliminate all other candidates on the found positions. e.g.:
As you can see in this example: the numbers 4&5 in row 6 are only possible on positions 6&9. Therefore: You can eliminate any other candidates on those positions, because you know you have to place the 4&5 on positions 6&9.
9. X-wings, Swordfishes, Jellyfishes & Squirmbags
These patterns are advanced patterns. In essence all 4 of these patterns come down to this. In N rows or Cols, a single number can only be placed on N positions. In this case the number can be remove as a candidate on the found positions on all other rows/cols. For example:
This is an example of a horizontal X-wing in rows 7&9. In these rows, the number 8 can only be placed on positions 4&9. Therefor if you know that on these 2 rows you have to share these 2 positions, the number 8 can never be possible on any other row on the same postition. Therefore you can eliminate all other candidates (8) in col 4&9.
A swordfish is the same pattern using 3 rows/cols & 3 positions. A jellyfish is about 4 rows/cols and 4 positions and a Squirmbag is about 5 rows/cols and 5 positions.
10. Nishio: Helper leads to invalid grid
Nishio basically means: Follow the forcing chain of sudoku constraints and see where it leads. When the site hints 'Helper Leads To Invalid Grid' this basically means that the forcing chain which is started if you enter 1 of the candidates leads to a grid. If you can find out which candidate is meant in the hint, you can eliminate that candidate. For example:
If you anlyze the helpers you will see:
So you can eliminate the 5 as a helper in cell 2,1
(did you get this example ? You can test yourself: If you know why the grid becomes invalid when placing a 5 in cell 2,1, you should also be able to derive why number 1 is the only possible number in cell 3,1!)
11. Nishio: Helper leads to solution
Nishio basically means: Follow the forcing chain of sudoku constraints and see where it leads. When the site hints 'Helper Leads To Solution' this means that from a cell there is a forcing chain to the solution, which is the most powerful hint you can get, because in this case although you might not realize it: you've almost solved the sudoku. Basically this is the Sudoku variant for 'Mate in 1'. For example:
In this case there are 35 cells left to fill. So it looks like you have a long way to go. However there is a one way solution in the form of a forcing chain starting from the highlighted cell:
And you will see that the filling of these cells will have forcing chains in them themselvers:
12. Forcing Chain: All candidates lead to elimination of same helpers in other cells
Sometimes you don't know which candidate is the right one in a cell. However if all candidates share the same effect on any other cell, you can apply that effect on that other cell. Take this example:
Now take a look at the forcing chains starting from cell 5,1:
So although you do not know which value to choose for cell 5,1 (step 1): Step 2&3 will always be the same. Therefore you can safely apply the effects found in step 2 & 3, leaving the original cell unchanged.
(Background info: The pattern in the upper 3 cells of the top centre 3-by-3 box is also called a naked triple. As is illustrated by this example: A naked triple can also be found by using the forcing chain technique)