Donald Miller Jr. spent yesterday afternoon lying by the side of a pool, an event notable for its rarity. It was his first day of relaxation in weeks, since he formulated an ambition that has become the driving force in his life.

The goal may seem unrealistic for a 19-year-old who has been a jockey less than two years, but Miller aspires to be the top race-winning rider in America during 1982. And the kid from Jessup, Md., does indeed have a chance to do it. He has already ridden 171 winners this year, three fewer than the leader, Chicago-based Pat Day.

This success may come as a mild surprise to Marylanders who watched Miller when he started riding at Laurel in the fall of 1980. He was no great prodigy; he was not hailed as the second coming of Steve Cauthen. But he did have a solid foundation for his chosen career. Encouraged by his father, a small-scale trainer and former jockey, he was 5 years old when he sat on a horse for the first time and 14 when he began galloping thoroughbreds.

Miller was so well-schooled that he started winning races in Maryland almost immediately, and with regularity. He won more than any apprentice in the country in 1981 (although the Eclipse Award for the best journeyman rider went to New York's Richard Migliore.)

Miller's principal virtue was his patience, his ability to sit in the midst of heavy traffic during a race, to avoid panicking, to wait for a hole to open. But he had some perceptible deficiencies, too. He did not always have the best control of his mounts, and he drew so many suspensions for careless riding that Maryland racing fans began to wonder whether the stewards had some kind of vendetta against him.

There have been plenty of riders who started with Miller's degree of ability, enjoyed great success as apprentices while they had that important five-pound weight allowance and then disappeared into oblivion when they lost that weight allowance and trainers stopped seeking their services. But this common fate did not befall Miller, partly because of his own intelligence and character, partly because of the great career break that every young rider dreams of.

Miller is consciously trying to learn the diverse skills that make a good rider. "I'm learning to keep a little more control. I'm paying attention to track biases. I'm learning to watch what goes on in a race besides my own horse. I'm learning a lot about the other riders."

While a natural like Cauthen might have some mystical knack to get horses to run well for him, Miller approaches the problem analytically. "I'm still learning to get a horse to want to run," he said. "A lot of times you'll get a horse who's kind of sour and not running good. So you talk to them, you pet them, you try different kinds of holds on them to get them where they want to run and pull you around, rather than make you hit them and get them even more sour."

Trainers understandably liked Miller's attitude, and he rode a few times for Ron Alfano, one of the two men who have been dominating Maryland racing in recent years. At a time when Alfano's regular jockey, Vincent Bracciale Jr., was hurt, Alfano tabbed Miller, who repaid the favor by winning a lot of races. Miller's agent, Gordon Becraft, said, "I thought that Jimbo (Bracciale) would get the job back when he came back. "But when I asked Alfano, he said, 'Don't worry, you have the job.' "

That job guaranteed Miller success, even after he lost the apprentice's weight allowance, because Alfano regularly ranks among the top race-winning trainers in the nation. Alfano is the leading trainer at Delaware Park now, and his horses have helped make Miller the leading rider.

As his victory total grew, Miller started looking at the national standings and seeing his name advance higher and higher on the list. So he and Becraft decided to make the big push.

They have been working on a grueling seven-day a week schedule this summer, operating at Delaware five days and at Laurel on Tuesday and Wednesday when Delaware is dark. They will continue working for their objective until the end of 1982, when Donald Miller's name may be added to names like Shoemaker, Cordero, Velasquez and Cauthen on the list of national riding champions.