I have a Pioneer PL-740 turntable that works extremely well, except there is zero damping when either lifting or dropping (and I mean dropping) the needle. I know there is generally a hydraulic oil that accomplishes this task. How do I repair this problem? Thanks, Dennis

You need to clean out and refill the tonearm lifter cueing damping fluid, http://www.turntablebasics.com/silicone.html
The cueing arm that lift and lower the tonearm is filled with Silicone damping fluid which will dry out with times.
You can also Google Silicone damping fluid.

Most turntables actually only dampen during automatic play and return (eject) not when manually manipulating the needle. Better turntables will have a counterweight at the back of the arm behind the pivot point, but that is to decrease wear on the vinyl and increase needle life and audio fidelity in the higher end.
Some turntables have a lifter arm that is dampened, but if your player doesn't have such a mechanism, or if it has one and you choose to manually manipulate the needle without it's usage, there is no dampening.
The fix unfortunately is to buy a turntable with a dampened lifter arm, and to use the arm when lifting and lowering the needle.