A runner at first wants to advance into scoring position, which begins at second base. His biggest impediment is the pitcher holding him on. A runner's ability to read a pitcher's rhythm is his best bet for reaching second.
An interesting notion—the pitcher holds the runner on by holding his own motion, varying his timing, and by not revealing his decision before he physically commits to it. The challenge to the runner is to read all of that, to judge when a pitcher will repeat himself or contradict his last action, and to recognize when the pitcher tips his decision to throw home (or throw over) before he actually does it. The objective is a better jump for the runner, out or back. The higher you go in competitive levels, the finer that point is sliced.
With a righty throwing, the runner at first has to watch the pitcher's back foot—the one on the rubber. Since the pitcher has to clear the rubber to throw over to first, any movement of that foot off the rubber is the runner's clue to dive back. Any other motion*, and the pitcher's throwing home, so the runner can jump out to his secondary lead, leaving quickly but not going too far. The best baserunners make that a seamless motion, out and back or out and gone.
(*The most common exception is with a runner also on third, where the pitcher ingeniously steps toward third to fake a throw, then spins to throw back to first. Works every time, right?)
With a lefty, it's trickier for the runner on first. Facing first, a lefty pitcher can throw there from the rubber—so the runner has to watch his front leg. If it crosses over the perpendicular, the pitcher's got to throw home. But there are degrees of leeway there—he can't step toward home and throw to first, but he can split the difference within reason. It's a matter of inches and umpiring judgment, and you hear dugouts barking "that's a balk!" all the time...one way to rattle a young pitcher.
At lower competitive levels, oblivious runners often get picked by straying off the base while peering at the thirdbase coach or the dugout for a sign. Good runners watch the signs from the safety of the base, and then get their lead. Two wide strides out plus a little more—within diving distance of the bag—bring a runner to a decent lead from first. He balances there on the balls of his feet, shoulders squared, arms poised and relaxed. He keeps his eyes where they belong, on the pitcher, looking for that movement that means release or get back. He reads a pitcher's abilities, using them to measure his own lead and to time his own movements. With a pitcher working his own clock, it's a battle of wits—a game within.
There's more to say to a firstbase runner: on a batted grounder you're gone; on a line drive you freeze until it's through the infield; on a fly ball you're going halfway and reading it. With two outs you're just plain running. The best baserunners aren't always the fastest, but those who get the best read on the pitcher and on batted balls, and who know how their own speed matches up against outfielders' arms.