The best way is to install the drip edge only along the eaves first, then place ice-and-water barrier (in the snowbelt) or felt paper (underlayment) over the drip edge. This lets any water that gets on the roof run down the underlayment and over the drip edge.
Once all the underlayment is applied, go back and place the drip edge along the gable ends of the roof. Covering the ends of the ice-and-water barrier or felt paper with drip edge ensures that windblown rain that gets under the shingles will run over the underlayment, not on the sheathing. The drip edge also helps hold down the felt paper to keep it from blowing off before you install the shingles.
But save yourself some aggravation and get the corners cut on the gable and eave pieces so they mate properly before installing them. That’s the only way you’ll get clean locking corners.