If your man starts heading deep and you hear an up-call, you have to assume the thrower is putting up a huck...so, obviously, you've got to try to beat your guy to the spot.
Back to Ultimate 101 for a second: if you were guarding the last guy in the stack, you probably have last-back responsibilities. An unguarded deep look is a lot more dangerous than an open under cut, so make sure the deep is shut down first. That means if you haven't communicated to your next deepest defender that you are going to follow your man in, you've got to remain the deepest player on the field, and not get sucked underneath.
Now from the point where you're one on one with your guy as he goes out...when you hear the up-call, I would not turn to find the frisbee at first. More than likely, your guy is going to take you in the direction you need to go—it's most important to stay with him until you have the chance to find the frisbee without losing a step. Therefore, accelerate with your man, and once you get up to speed, then turn your head to find the disc. Since you just followed this guy underneath (and were facing the handlers), you should have a pretty good idea where the throw is coming from—at the least, you know which side of the field the disc is coming from. This information will let you know which shoulder to look over (if it's not obvious).
It's important to make as quick an assessment of where the disc is going as possible—you don't want to be running downfield looking backwards (I don't know much about proper sprinting form, but something tells me this isn't going to get you moving as fast as possible). Take a peek, then get your head back around and sprint—look back again only periodically. Each time you locate the disc, be working to out-position your opponent. Whoever takes the straightest line to where the disc ends up has the best chance of making the play.
In the event that you're guarding a more athletic player, you are most likely going to want to force that person underneath. That means when he cuts in, you follow him in with the intent of staying close, but not to try to actually get in front and get a block. Your first priority is preventing this player from beating you deep—again, giving up a 10-yard gainer underneath is better than a huck over the top. So since you're following him in, when he stops and turns to go out, you're now a step ahead of him. Use your body! Do not be afraid of contact here—make him run through you to get deep. As he turns around he's going to have to get around you, so block his path. If he tries to get around your right side, step right. If he goes left, move left. Move your feet and be ready to turn your hips to run downfield. Get in his way to stop his momentum, then (or at the same time) turn and accelerate!