Most people will probably laugh about this. But this is truly something that I did to help teach myself better driving habbits for maintaining a higher fuel economy. Get A plastic 2 liter of soda. Simply place it standing up in your passenger floor board. If you drive without knocking it over, then you are conserving fuel. This goes for starting and stopping. Trust me, the aggrivation of standing it up over and over again will teach you to drive right. And not to mention your soda wont spray you in the face when you open it. Silly I know. But it does work!
alvaro84 is correct. It depends on your vehicle. Take my 4wd pickup truck. If I drive it like there's an egg under the go pedal, it gets awful mileage. In that vehicle, its much better to just give it 1/4-1/2 throttle and just get in a higher gear faster, than to spend a considerable amount of time in the lower gears by pressing the pedal lightly.
Braking hard can save fuel too. Depends on the situation.
Red lights (or temporary slow traffic) appears ahead: braking hard to reduce the speed to maximize the minimum speed you will have until you reach the lights they have turned green and some of the momentum is saved. If you reduce speed slowly (approaching with higher average speed) you might have to stop and then accelerate from standstill because you will reach the lights before they change (or before the traffic ahead picks up speed).
In many cases fast but accurate reactions are better than slow ones.
I used to drive aggressive in my Accord, and I switched to avoiding the brakes, and smooth slow driving and got ~10 mpg better. Smooth isn't a bad thing. More rapid acceleration can help automatic more because of the lockup torque converter deal. I learned the smooth part first, then moved on to more brisk, low rpm acceleration that you can force with a manual.
Oh, and learning to anticipate conditions up ahead is certainly something that can be learned from the bottle trick...
And this is the most important in city traffic.
Other than that, my first vehicle is Teresa - a 650cc motorcycle (50hp/62Nm for 187kg). Being very light for her strength, slow and smooth acceleration, especially in lower gears mean ridiculously low load to that engine. Firm handling of the throttle (and early shifts) puts me at a waaay more favorable place of the BSFC chart.
If I handle the YARDIS the same (1-liter 67hp/90Nm engine for 840kg), the result is pretty smooth But the gears are disturbingly short and close to each other, so I often skip a few of them... 1-3-5, or even 2-5 (not from a dead stop) are typical patterns to me. I just want to get into 5th as soon as possible.