I dislike my job & want to quit. I'd like to do it in a time frame that works for me, but I'd also like to do it in a way that's not offensive to my employers & allows them ample time to find a replacement. What's the best way - & the Jewish way - to address a touchy situation like this?

As reflected in the Ten Commandments, which describe specific obligations first to God and then to our fellow man, we are obligated to treat people with honesty and dignity.  As the great rabbinic sage Hillel states, “Whatever is hateful to you, do not do to others” (Shabbat 31A).  This, along with the provisions of your work agreement, should be your guide in this situation.   

It is laudable that you want to “do the right thing”, which is to leave your employment with minimal harm to your employers.  Unless you signed a contract which would only allow you to leave with specific cause, there is obviously nothing wrong with quitting.  It is important that you find satisfaction in your work, but as you rightly note, that doesn’t mean that you can take advantage of your employer.  Jewish law mandates that we follow the law of the land in all civil matters, which covers employment.  Almost all agreements have provisions covering when you need to give notice before leaving your job, which you should follow.  As long as you are doing your job to the best of your abilities, which is what each employee owes his employer, you can decide when you want to give notice i.e. once you have another job lined up.  Thank your employers for the opportunity they have given you, and let them know that you will be happy to help your successor in the transition.  As long as you follow the provisions of your agreement and common sense, you can be sure that you are following the best and Jewish way of leaving work.  Good luck.