"Efficient" means having a high ratio of output to input. Efficient also means means working or producing with a minimum of waste.
Example 1: "An efficient test engineer wastes no time".
Example 2: "An efficient engine saves gas".
"Effective" means producing, or capable of producing, an intended result; or having a striking effect. Example 1: "For automated testing, WinRunner is far more effective than an ordinary oscilloscope". Example 2: "For rapid long-distance transportation, the jet engine is more effective than a witch's broomstick".