About 30 years ago, I was trying to learn to swim the entire length of a 25y pool underwater. When I first began, I assumed that the best plan would be to swim as fast as I could, since this would minimize the amount of time for which I would need to hold my breath. But I soon learned that it was actually better to swim at a relaxed pace, since this increased the time before I needed a breath more than it increased the time it took me to go 25y.
It definitely helps, too, to take some very deep breaths right before you begin. Werner's suggestion also makes sense, since it is primarily the accumulation of carbon dioxide in our lungs - not our need for oxygen - that prompts us to breathe.