When I hear the up-call, my first instinct is to get between my player and where I think the disc is going to be. I don't look for the disc yet because the disc is secondary to my player when I'm on defense. If I can get my body into the proper position, I will get the disc every time.
Typically in this situation, I will try to make some kind of body contact (not with arms or legs)—jockeying for position using my butt or shoulders to maintain my position between my player and the disc. This is something that changes from game to game in what will be called a foul and what will not. I appreciate games in which some contact is allowed so that contact similar to what is usually used in soccer for shielding the ball is appropriate.
Information that is important to me when trying to establish my position includes: type of throw (forehand vs. backhand, inside-out vs. outside-in), handedness of the thrower, power of throw, float of throw, and wind. All of these things will affect the flight pattern of the throw and thus where you should position yourself. You should know some of these things immediately—if the throw is on the live side, you know it is a forehand if you are forcing forehand. The one hitch to this is if the thrower is left-handed. To be a great defender, you need to check in with who has the disc at all times so that you know whether a forehand or lefty backhand will be coming up. You should always have the force of the wind noted in your mind at all times during a game so that you don't have to lick your finger and test it while trying to get a D. The power, flight path (IO vs. OI), and float of the throw are all things you should be able to read by the first time you see the disc in the air.
After hearing an up call, I typically take 3-4 hard sprint steps to catch up to my person before I check in with the disc. Then, when I do check in with the disc, it is a brief look during which I can see how high it is, how fast it is going and at what angle it is flying. The person I'm guarding doesn't come into my mind that much as I try to establish position.
If you have all the correct information and have the right body positioning based on this information, you will be able to get the D every time. You don't have to worry about jumping higher than someone unless they are significantly more athletic or taller than you. If this is the case you might want to jump earlier to get more of your body between them and the disc (and they will also probably going early). If I am similarly athletic to my offensive player and in proper position, I will go for the catch with both hands to make sure I get the D. However, if I haven't had time to get in the right position, I will go with one hand over or through the hands of my player to reduce the risk of fouling. If the huck goes up to the break side, I spend more time sprinting to get position and reading my player than I spend reading the disc itself because as the saying goes on defense, "Play the player, not the disc." As long as they don't catch it, you did your job.