Short answer: It depends on the car. Trial and error testing is your best tool.
Long answer.
The best average fuel efficiency will come from optimizing the applied engine torque (as measured at the wheels) verses fuel consumed throughout the velocity change curve (holy technical talk, Batman, doesn't that sound intellectual!). In other words, for any given car it will generally depend on the engine RPM/torque curve coupled with the transmission gearing vs. actual fuel consumed.
The idea is to spend as little time in the lower gears as possible without lugging the engine (everyone know what the phrase "lugging the engine" means, right?), and then once the engine shifts to the highest gear, ease off the gas and gradually gain speed after that point. A rule of thumb is that most engines develop their best torque efficiency around the lower third to half range of the rated RPM. So, most typical ICE powered cars should get their best gas mileage through the lower gears somewhere between 1,500 to 2,500 RPM. If you are accelerating hard enough so that the engine revs past 2,500 RPM in this hypothetical example then you are probably not getting the best mileage.
In my case, it seems I realize the best gas mileage while accelerating between 1,000 and 1,700 RPM (this is not a hybrid car BTW). So, I accelerate modestly and ease off the gas once the engine RPM gets to 1,700. After the transmission shifts, I get back on the gas -- not enough to make the transmission shift down a gear -- until I get back up to about 1,700. And so on and so on. After the final shift into high gear (which happens at about 35
MPH), I poke along gradually gaining speed until I am up to my goal.
Of course, all other things being equal acceleration to a given speed is a trade off with time. You will always get better mileage once you are in high gear if you accelerate slowly and practice long and slow speed changes while in high gear.
Now, if you have one of these new fangled constant velocity transmissions then same considerations apply, you just have to know the RPM torque curve of your engine vs. fuel consumption and adjust your acceleration to maintain an appropriate engine RPM.