Puzzles take a lot of patience.  In order to complete them effectively you must adopt a strategy or group of tactics.  Identifying the edge pieces is a pretty good first move.  It reduces the dimensions in which a person might combine the pieces to one, since the edge can be viewed as a simple continuous line.  Grouping the pieces by color can allow you to narrow the pool of pieces that have to be considered.  Also, by looking at the box photo pieces can be grouped by geography, or where those pieces are going to end up in the final product.  Most really difficult puzzles eliminate one or more of these tactics by printing on both sides, using false edge pieces, not including a final image, or contain large tracts of repetitive color.

This Lord of the Rings puzzle my daughter and I are powering through had numerous helpful features that led us to complete it rapidly.  The edge of the piece of artwork has a border that not only allows you to complete the edge pieces easily, but also add a comfortable margin to that edge.  Banners naming Boromir, Faramir, Gandalf, Frodo, Gollum, and others allow you to identify the location of lone pieces pretty easily.  And a variety of distinct colors means you can start separating this puzzle out into pretty small piles of related pieces.  You're not going to mistake the orange of Faramir's shield for the bright orange of the flaming ring, and there's no mistaking the Black Speech written on its circumference.