On a shortboard, you have to start your paddling at a different point on the wave. Position yourself in the lineup so that you are closer to where the wave breaks. When you find a good wave, balance yourself so the board is trim, just like on a longboard and paddle your heart out. It will take a while to get used to the timing, of course, but you should be able to pick it up pretty quickly.
Instead of "popping up" think explode up...you want one fast move from paddling position to standing up. This is where core muscle strength (abs!) is important. Be sure to have your feet centered over the stringer when you get up, too. There is a lot less room for error on a shortboard.
Also, if you are on a steeper, faster wave, when you catch it the nose of your board will be out of the water and you might be tempted to push it down before or as you stand up. Don't. This will send you over the nose really fast.
If the wave is crumbly (not steep), and you are trying to catch it on a shortboard, it will be harder to get enough speed. One thing that helps me on this type of wave is to put my hands flat on the deck of the board instead of grabbing the rails when I am ready to stand up. It gets rid of a great deal of drag.