Diet, exercise, enough sleep, and a good social support structure are pretty much the keys to good health in general. The fact that we have so many health issues in western society are because its so easy to neglect these things.
Exercise (specifically, aerobic type) is the main thing you need. A good exercise regime gives you a lot of leeway in the diet aspect especially if you don't overeat (since your caloric burn will be high enough on the regular to not have to deal with issues like too much carbs). It also helps you sleep as you get tired and can fall asleep easier, and reduces stress levels, which is very important in regards to longevity.
There also have been studies that link brain function deterioration with lack of oxygen, and people with higher VO2max values are at a lower risk of cognitive decline.
Something as simple as cycling to the office instead of taking the car can have extremely positive effects.