Do you watch any cooking shows on TV? That's actually a good way of learning basic technique.
But speed only comes with experience. You should be concentrating on 1. learning how to hold the knife and food properly; and 2. accuracy. With those two, speed will come in time.
The most basic way of holding a knife, particularly a large one, is the pinch grip. Essentially, you choke up on the handle. The blade, itself, is pinched between your thumb and index finger while the rest of your fingers curl under the handle to grip and support it.
You might find yourself instinctively laying your index finger along the top of the blade. Technically this is incorrect. And for long-time knife work, as would be found in a professional kitchen, it's fatiguing. And there's a loss of control. But for the home cook, if you're comfortable that way, I don't see any reason not to do it. But the pure pinch grip is actually more efficient, especially when chopping.
For chopping, such as when mincing herbs, you use your off hand to hold the point against the board, and your strong hand to lift and lower the knife into the foodstuff, rolling it along as you chop.
For most other things you want to learn this sequence: block, plank, stick, cube. Always start by creating a flat on whatever you're cutting. Let's say a potato. Make a thin sliver along one long side to create the flat. This assures a stable platform as you make your other cuts. Now, make a slice along one side, turn the potato onto that flat, and do it again. When you've done all four sides you will have made your block. In a fine restaurant the goal is to make that into a perfect rectangle. But in the home kitchen it's not so important.
Now, with the potato on one of the flats, make a slice as thick as you want. For discussion sake, shoot for 1/4 inch. Make a second slice, trying to make it as even as the first. Do the whole spud that way, and you'll have created your planks.
Next. Take one of those planks and lay it flat. Cut a stick-like slice from it, making it as close to 1/4 inch as you can. When you're done you'll have made your sticks. Eventually you'll be able to do this by piling all the planks up and cutting them at once. But, initially, do just one or two at a time, until you develop the feel.
Next, take one of the sticks and cut it to form 1/4 inch cubes. When you feel confident, do the same with several sticks at a time.
There are names for the various cuts you've made, based on their size. But you don't have to learn them unless you want to. For the average home cook, for instance, all "sticks" are julienne cut, even though that technically refers to sticks of a precise size.
The only other thing you have to learn is how to hold the foodstuff as you cut it. That comes from your off hand. This is easier to see than to describe, but, essentially, you'll use your off hand sort of like a claw to grip and stabalize the item. Your index, middle, and sometimes ring finger will be on top and slightly to the sides of the item, leaning forward so the fingertips are out of the way. Your thumb should be safely behind your fingers as it helps grip and move the item.
Now, using your knuckles as a guide, lay the knife in place and make your cut. Move your hand back slightly, and make another cut. Etc. What you're actually doing, each time, is moving the knife along the item, with your knuckles acting as both a stop and safety shield.
That's all you really have to know. The rest will come with time in grade. But you'll be surprised at how quickly speed develops.
