It all depends upon the situation. If you study the concept of "opposition," you will learn the strategy for playing for the draw (by creating a stalemate position) in King plus Pawn vs. King endgames. Played correctly, the opponent will end up either having to stalemate your King or lose the pawn ( a draw by insufficient material to mate).
Stalemate strategy
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Get rid of all your material, or get it "locked up" so you don't have any moves besides yur King.
Looking for a stalemate combination is just like looking for any other tactic. So always look for any tactics before resigning, and only resign if can you find nothing sensible you can do. No reason to continue if you can't find a continuation.
As a strategy eddiewsox's suggestion is a possibility, it kind of narrows down what stalemate is all about. But I would say that it is a good idea to evaluate the position and judge whether it is a good idea to continue like that or whether it is a waste of time instead of resigning.
Here is an example where you can force a draw because of a stalemate situation:
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In a losing position, is there a known strategy for achieving a stalemate, rather than a checkmate?