A good playtest should have conscious goals in mind. In my experience, the nature of these goals changes as time goes on. Playtesting can be broken into stages.
First, there are usually solo trials to test out game mechanics and refine the overall theme of the game. These may be split into mini tests to see whether a particular aspect will work. In ITTBZ for example, this involved refining and ultimately eliminating a weather mechanic that was a base part of the early game.
When solo testing indicates that the game is playable, it's time to invite other people. It's important to have open minded playtesters who will be willing to give constructive feedback and realize the game is a work in progress. The key to this phase is to determine: is the game fun and does it have potential. If the answer to either is no, it may be time to scrap the idea or radically rethink it.
If your game survives this far, you enter intensive regression testing. This means shoring up any weak spots and making sure the mechanics are rock solid. A later subphase involves searching out and correcting any minor niggling errors.
Usually the intensive playtest involves a core group of people who are able to dedicate the time to play regularly. In this last phase, it's time to spring your baby upon the world. First, introduce the game to people who have never played before. Often explaining the rules to a fresh set of ears will bring up questions or ambiguities that have gone unnoticed up until this point. Finally, have people play the game with no assistance from you, relying solely on the written directions.
Obviously the fine tuning of a game may continue even beyond when it is published. Keeping in mind the outlined sequence of testing can help you get to that point. It's a long journey from concept to complete game, but in the end it's worth it to sit down and play your very own creation.