In this game against Max Judd his attack on both sides of the board makes the game look simple. The final combination seems to come out of nowhere, but it was the result of something many players don't seem to grasp. Spielmann once observed he could see a combination as well as Alekhine, but he just couldn't get the positions Alekhine got. So many of Morphy's opponents lost quickly even though they were also excellent tacticians because they made strategic errors that left glaring weaknesses in their positions.
The first thing that has to be done is examine the position for a sound forcing move, but if one can't be found, and usually they can't, a player must then find a plan. A "plan" is NOT a particular motif that is present throughout the whole game. For example, in the Exchange Variation of the Ruy Lopez white's Q-side P-majority will be a major factor if he reaches the ending, but that is only one factor in his planning because other factors may override it.
When there is no sound tactic available one must do something constructive and short term plans, often consisting of no more than 3-4 moves, are often employed by the master. If there are no forcing moves in a position you won't be able to calculate more than 2-3 moves into the future and in those cases there is a great emphasis on the correct evaluation of the position based on positional factors. Another thing is that in games between amateurs, unlike masters, the two players often won't be calculating along the same lines anyway. Often strong players are calculating along the same lines but the their evaluation of the position is different. In any case, the trick is recognizing when exact calculation is required and when it's safe to embark on a short-term plan.
Barring a serious blunder, which is what most amateurs seem to be waiting for when they think of tactics, the master builds up his position slowly. Strategy is often nothing more than a series of moves (sometimes no more than two or three moves) designed to reposition a piece to a better square or occupy an open file with a R and such. Purdy (I think it was) advised that when you can't think of anything to do, look for your worst placed piece and try to find a way to improve its position.
Then right when it looks like Judd has gotten himself a nice position where he controls the e-file and has successfully blocked Pillsbury's R on the d-file while at the same time threatening a N fork on f3, Pillsbury sacs his R for the well placed N and finishes the game with a mating attack. An explosive conclusion by Pillsbury!