What is fore foot striking?
Transitioning from a heel strike to a fore foot strike is a huge change in your running mechanics. Having done both they feel as different as running is to walking. When you land on the heel your knee is the only joint that can flex to soften the landing. Then as the foot pulls through you flex your ankle joint and push off of the fore foot. The pattern of movement for each step would be heel-toe. This is demonstrated in the top picture below (you can ignore the graphs, I just wanted to use this picture to illustrate the foot motions.)
Notice the extra motion in the latter case: you have another ankle flexion, this time on the landing in addition to the liftoff. This is why it is a completely different form of locomotion. I'm not going to get into the science of loading forces because the data on that is contradictory and inconclusive. But I can speak from experience that it feels more fluid and powerful than landing on the heel, which is why I decided to make the switch.
What do you need to run this way?
You might be surprised to learn that minimalist running isn't new at all- only the name "minimalist". Elite runners in the 70's and 80's always used racing flats and landed far forward on the foot. The reason is that it is a much more aggressive, faster style. You can't run 4-minute miles landing far back on the heel, it is much too sluggish.
The reason that these men had no problem running this way was because they were professionals so they were built right: thin, long bones, low body fat, and highly muscled. This is what it took to run fast back then and this is what it still takes today. The degree to which you can become built like a professional runner will be the degree to which you can run easily while landing on the fore foot.
Another thing you need is improved coordination. Bending at the ankle as well as the knee as you hit the ground takes practice. Also your cadence tends to be higher when you run this way, so your nervous system needs to be able to go faster to process all of this new movement.
Shoes also make a big difference. It is uncomfortable to land on the heel without extra cushioning, so wearing a thin shoe will automatically encourage you to land on the fore foot so that you can utilize that extra ankle bend I discussed earlier.
How do I make the change?
It takes time to develop the strength and coordination that I described above, but the new shoes is a quick fix. Go to a running store and try on different pairs until you find one that fits your feet well. You want something with little cushioning and little support and a small if any heel-to-toe drop. If you can easily twist the shoe in your hand it is the right kind; if it feels stiff and thick like a two-by-four that won't help you make this switch.
You have to start slowly with this new form because it uses such different muscles (it is much more demanding on the lower leg, ankle, and feet.) I was sore after just one minute of running with my new shoes. I did that for two weeks then switched to two minutes, four minutes, and so on until I could run a couple of miles at a time. All in all I'd say it took me six months to get to where I could easily run for twenty minutes and not have sore calves the next day.
You will develop a lot of muscle just from the new shoes but I would also recommend strength training as well. Running uses all of the muscles in your body, from you feet to yours hips to your shoulders. I like Nike Training Club as an over-all weight-lifting program, but there are exercises more tailored to mimic the runners stride (check out these workouts. I've seen videos of Galen Rupp doing these exact motions, and they seem to be working out pretty well for him.)
Coordination just comes from practice. Focus on keeping your cadence high, be cognizant as you move through the running motion, and do drills that practice proper form. It's easier to run with a long, slow stride or a short, fast stride, but to run fast you need to have a long, fast stride, and it takes time to develop the ability to move your legs that swiftly.
Commitment and Growth
As you can see this requires a major life-style change. You need to commit to the new form, and although the commitment needs to be significant (at least several months) it doesn't have to be permanent. If you give this a genuine effort and your body never seems to adapt, then for your particular body landing farther back on the heel might be better and you could always go back to the way you used to run.
No one can prove that this is categorically better for every person, but I can only describe my own experience and imagine that other people will experience something similar. I noticed distinct, discontinuous changes in my running form and over-all strength as I moved in this new direction. I had one such moment last night: after taking a break from running to fix a piriformis injury my first run back I felt more like a flight than a run. Rather than trying to feel out exactly how long of a stride to take and how deep to bend into the knees, one specific motion felt like obviously the most comfortable way to move. And I went faster than I've gone in months. Minimalist running is a huge investment but the payoff is equally dramatic.