The meanings overlap, and both have specific meanings in certain technical fields. Generally, "effective" means "it works. It completely achieves the intended purpose." Cost and effort are ignored. For example, "Living in an English-speaking country for three years is an effective way to learn English." "Efficient" includes cost or effort considerations. "However, it is more efficient to take lessons; the cost of the lessons is small compared to living and travel expenses, and you will learn more, faster, for less money." In physics and thermodynamics, when energy is converted from one form into another there is some waste. "Efficiency" is the percentage of the input energy that is converted into output energy. If a car engine burns gasoline and produces 1 million joules of heat energy, and produces 300,000 of mechanical energy, it is 30% efficient. A car that goes 20 km. per liter of gasoline is "more fuel-efficient" than one that goes 15 km. per liter, it does more with less. Around the year 1900, in the US, a man named Frederick Taylor introduced something called "scientific management." This had to do with organizing work processes for maximum efficiency. He introduced techniques like time and motion study, trying to find the best, quickest, and least costly ways to do things. As a result, "efficiency" became a management buzzword. A byproduct is that "efficient" came to mean a general term of praise for anyone seen as a good worker: "my efficient assistant."

Effective means to be successful in producing a desired or intended result. While efficient means performing or functioning in the best possible manner with the least waste of time and effort. If you understand what I mean. :)