The most commonly-used approach to building a puzzle is to start by separating the edges from the inside pieces. Once the edges are connected it is easier to move inward. For those new to puzzles, it is recommended to choose one consisting of multiple areas with contrasting designs and colors. This enables the narrowing down of potential portions of the puzzle where a particular piece will fit.
One puzzle solving strategy is the use of the picture on the box as a guide. Once the edge is completed and the location of a particular piece is discovered (in the picture), it can be placed inside the overall puzzle at the approximate location it belongs. Done enough times and, eventually, interlocking the pieces will be possible.
Another approach is to sort the pieces by color, and work on one color at a time. When working large areas with the same color (such as the sky in many landscape puzzles), shape is important. All the pieces of a particular color can be laid in a grid and tried against other pieces in the grid.
Many large jigsaw puzzles have redundancy in their cut pattern. Many have 180 degrees of rotational symmetry around their centre point.
Puzzles of 1000 pieces also usually involve a smaller cut pattern that is repeated 4 or 6 times over the whole jigsaw, and that smaller cut pattern usually also has 180 degrees of rotational symmetry, so a particular shape may appear 8 or 12 times in the puzzle (although with truncation for edge pieces). It is possible to identify the presence of these symmetries or repetitions relatively early in the process of completing the edge frame. When redundancy is identified, it is possible to use already solved parts of the puzzle to identify the exact shapes of pieces required to complete other sections, greatly simplifying the search.[Source]
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