|Each of the numbers on the left side indicates how many cells are shaded in groups in the corresponding row. Between the groups there must be at least one cell that is not shaded. In the same way, the numbers at the top show the vertical groups. To solve a nonogram puzzle, it's usually most helpful to start with the biggest groups. Take a look at the numbers above and to the left and find the largest of them.
|The last line of the left column with the numbers is the number 5 (red). It indicates that this line has 5 consecutive shaded cells. Since the entire grid has a width of 5 cells in all, it follows that they should all be painted over. In the first line, we see the number 3. This might be across columns 1-2-3, 2-3-4, or 3-4-5. But wherever this block of three cells is located, the central cell in column 3 will be colored for certain. If there was a group of 4, we could safely paint the 2nd, 3rd and 4th cells of its row.
|Now we look at the numbers above. The first column is 1. It indicates that only one cell of this column is painted. Since we already have such a cell, we can tell that the rest will certainly not be painted, so we can safely use the right mouse button to put markers in those cells. Above columns 2, 3, 4, and 5 there are two numbers, therefore in each of these columns there will be two groups of filled cells. The bottom numbers in three of those columns are 1, and we already have one shaded cell at the bottom of each column, so we can put markers on top of the shaded cells to let us know there will not be another painted cell there.
|In the second column the bottom number is 3, hence the lower group consists of three cells. We already have one cell painted, and it's against the bottom edge, so we can add two cells above and put a marker on top. In the third column, where we already have one cell painted at the top, the upper number is 3. In this column, we can paint 2 more cells below the one already painted, so that the the top 3 are covered.
|In the third row, we formed a group of two cells. The first figure, 2, shows that we have fully painted this block, so we put a marker to the right of this group. In this same row, there is still a number 1 left to fill, and only one cell empty and unmarked, so we can paint it over. In the first row, which has only a number 3, we've already identified the first cell is empty. With only 4 cells left available, we can paint another cell in the middle. This is confirmed by the top number 1 in the fourth vertical column.
|There are very few cells left open now. Number 2 in the fifth vertical column shows that we need to add another shaded cell in this column. This block is now complete, so we put a marker on top. We've still got one open cell in the first row. Since we need 3 in this first horizontal row, it is necessary to paint it.
|Congratulations! The nonogram puzzle is completely solved! Color puzzles are solved similarly. The difference is that if two groups are of different colors, they don't need any white cells between them. Blank cells are optional, so they will sometimes be between groups and sometimes not!
If this explanation seems incomplete, and you are still confused, here are some instructional videos: