20-year umpire here. It's a noble calling, and you can devote pages to honing your skills to determine and have your antenae up for holding calls. Here's some key points, some mentioned previously, some that may help.
Presnap: Your keys are going to be C-G-C. You're going to be responsible for snap infractions so keep an eye on the ball. Then widen your view from the C to the two guards next to him.
Presnap evaluation: Look for mismatches. Look for the tiny lineman who's heads-up with the 300-pound tackle. He's the one who's most likely to have to bend the rules to keep the tackle out of the backfield.
Run/Pass: Immediately after the snap you'll be able to tell if it's likely a run or pass. An offensive line surge signals run. A line that takes a step backwards indicates pass blocking. React accordingly.
Shifting from your keys: Use your peripheral vision to ID where the play is moving. If the run is going to the left, start giving up the guard to the right to pick up blocking by the tackle and guard to the left at the point of attack.
Watch their feet: A good tip that a defender is being held is to watch his feet. If he's leaning at an unnatural angle but still managing to stay on his feet, there's only one way he's staying up - he's being held.
Watch YOUR feet: Don't move too much. That was the best learning I got at my first clinic. When you're moving, you're less focused on what you're seeing. Plant yourself 7-9 yards or so back and try and stay there. If a runner comes right at you - freeze. Make him commit to go left or right. Remember: You're the only one back there NOT trying to tackle him, so he should avoid you. Then just pivot as he goes by you and watch the action around him.
Double teams are rarely holds: Most umpires will rarely throw a holding penalty on a double-team block. But never say never. I've done it once or twice when the hold has been egregious. Just keep your eyes open.
Grasping: Grasping is not holding. In order for a grasp to be a hold, the defender has to make an attempt to elude the grasp of the blocker and be restricted from making his way to the ball carrier. As I often tell complaining defenders: "Until you try and get away, you're just dancing."
Make them big: A holding penalty needs to be big. A restriction at the point of attack that keeps the defender from reaching the ball carrier needs to be called; One on the opposite side of the field from a TE that was never going to get the ball carrier doesn't. That said. If someone picks up and throws that TE to the ground where everyone can see it, you've got to throw that flag. And take a second to tell the blocker what a dumb foul it was.
Be preventative: If someone grabs and restricts a defender well away from the play, tell him as he's heading back to his huddle (out of earshot of the defense) "Hey No. 74 - If the play had come to your side of the field you would have cost your team 10 yards." That lets them know you're watching; you see what they're doing; and they shouldn't do it again.
NEVER ball-watch: There's rarely a need for you to watch the football - A football never commits a foul. Watch the blocks on the line. As the ballcarrier comes toward you, watch the blocks in front of him and immediately behind him. After he's gone, watch the trailing players for cheap shots. On sweeps toward the sidelines, watch for action away from the ball. Umpires are never off-duty.
