Scheduling the first four primary contests for February 2016, so that those states (Iowa, New Hampshire, South Carolina and Nevada) don't hold their contests any earlier in January or December.
Holding their convention earlier, at some point between late June and mid-July. Campaign finance laws forbid nominees from spending funds raised for the general election until after the convention. Moving the convention forward allows the nominee to spend those funds much sooner, so he or she is not defenseless against attack ads through much of the summer, as Romney was in 2012.
They also want to avoid having a primary that is decided in one day or even a few weeks. If the primary is too short, it gives an advantage to candidates with more money and name recognition, and does not vet the party's nominee as thoroughly.
Penalizing heavily any state that holds its primary before March 1, by taking away most of its delegates to the convention. Loss of delegates means that candidates don't have an incentive to come to your state. It's also likely your delegation to the convention ends up in a hotel located farther away from the convention hall, and with the worst seats inside the hall.
Exempting the first four states from those penalties to prevent any mutually assured destruction affect. For example, without exemptions for the first four states, another state like Florida could try to leap-frog ahead of them on the calendar, knowing that any penalty it might face would be negated when the first four jump back ahead. Without the exemption, the penalties are far less meaningful.
Requiring any state that holds its primary between March 1 and March 15 to award its delegates to candidates proportionally, according to the percentage of the vote won rather than awarding all of them to the winner. This allows candidates running second or third after the first four states to stay in the game and in the delegate hunt.