Nonograms are solved by going back and forth between rows and columns. Each line is solved as much as possible from its clue and the cells already known, and every new cell gives information to the crossing line.
The overlap method
In a 10-cell line with clue 7, the block can start at the earliest in cell 1 and at the latest in cell 4. Cells 4 to 7 are covered in both positions, so they must be filled. The bigger the block, the more overlap.
Simple sums
Add the clues plus one gap between each block. If the total equals the line length, the line is fully determined. For example, clue 3 1 4 in a 10-cell line needs 3+1+1+1+4 = 10 cells, so there is only one way to place it.
If the total is a little smaller than the line, the difference is the 'slack'. Any block longer than the slack has cells that must be filled — the overlap method applied to the whole line.
Use the edges
If a filled cell touches the edge of the grid, it must belong to the first (or last) block of that line, so you can extend it to the block's full length and add a cross after it.
Cross out what is empty
When a line's clues are all satisfied, cross out every remaining cell. Crosses prevent mistakes and often unlock the crossing lines.
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