I can only answer this about the forklifts that I have operated. There are probably different designs than the two I have used, but I believe that knowing the basics should allow you to operate almost any you come across.
First, let's discuss the operation of the forks themselves, as those controls seem to be fairly standard. You will normally have 2 levers. One lever controls the height of the forks. On every one I have operated, you pull back/down to lift the forks and forward/up to raise them. Different models have different heights.
The second lever controls the front/back tilt of the forks. This allows the weight of the object being carried to be shifted back slightly (toward the fork frame). If you are moving an object over a distance, you want to have the forks tilted back so that the object doesn't fall off the front. It also allows you to remove an object from the top of another obeject without scraping the top. When you want to place the object you are carrying on top of something (or on the ground), you tilt the forks forward and back out from under it. The downward-tilt of the forks helps the object slide off.
Some models have a third level that controls the width of the forks. For some large objects, you want the forks to be spread apart farther to provide more stability. Smaller object may require that the forks be closer together so they fit under it. Models that don't have a lever to control this have to be adjusted manually. This is normally done by lifting the fork by hand, moving it, and then locking it in place where you want it.
Now that you know how to work the forks, let's move on to driving the forklift.
I have operated forklifts that use a clutch and ones that don't (hydrostatic drive).
The clutched models have a gear selector, normally located on the steering column, and a fuel-burning engine, either gasoline or propane. The model I drove had two forward gears (slow and fast) and one reverse. Driving was as simple as picking the gear, holding the clutch in, and then releasing the clutch as you pressed the gas, just like driving a manual transmission car.
The brake pedal served to slow the forklift, although releasing the gas and applying the clutch worked just as well. The brake also locked in place so that the forklift could be held stationary.
The other model I have used emplyed a hydrostatic drive, which, simply, means that you press the gas to go and release it to stop. If you let up on the gas quickly, you stop quickly....you don't coast using a hydrostatic drive.
The interesting thing about the model I used was that the battery powered engine only ran when the gas was pressed. Once the forklift stopped moving, the engine shut off. You started the engine again simply by pressing on the gas.
The hydrostatic model had two gas pedals, forward and reverse. When you wanted to reverse, you let off of the forward accelerator and pressed the reverse pedal.
Now, lets go though a quick rundown of how to pick up something and move it....we'll assume the manual transmission, because it is a little more difficult.
First, start the engine with the key, usually on the side of the steering column. Hold the clutch in and move the gear selector to "Low". Now, press the gas and begin releasing the clutch. One you are moving, use the clutch and gas to control your speed.
Approach the object you want to pick up as straight as possible. We'll assume you are picking up a loaded, wooden pallet. Use the fork-height lever to bring the forks to the level of the pallet. Ensure that the forks are level using the fork-tilt lever. Drive forward slowly until the foks are under the pallet, and the pallet is aginst the back of the forks.
Lift the forks slightly and tilt them backwards so that the load rests against the backstop of the forks. Once the forks are tilted back, lift them a little higher to clear the object below them. Back the forklift slowly until you are able to lower the pallet. Lower the forks so that the pallet is close to, but not touching, the ground.
Now, drive to where you want to put the pallet you are carrying. Make sure you get lined up so the pallet will be placed squarely. Lift the forks up (still tilted back) to the height you need and drive forward slowly. Once the back of the pallet you are carrying is where you want it, lower the forks so they are just above the object you want to put the pallet on.
Finally, tilt the forks forward so that the pallet is touching the object it will be placed on. Back up while lowering the forks slightly, and the pallet should slide off without getting caught on the forks.
Hope that helps...