To expand on Kneale's post:
|How do you turn going downhill quickly and on a dime, like in moguls or slaloms.
This is done by keeping the upper body facing more down the hill and turning the legs, feet and hips (partually) under it. Both skis must be turned the same direction at the same time. It could be done in a wedge, but it is easier parallel.
|How do you stop quickly and on a dime like after a downhill run.
The manuver is called a hockey stop and works much the way a hockey player stops suddenly. It is done by pivoting both skis 90deg to the direction of movement (while flat on the snow) and then progressivly adding edge angle as the legs absorb the energy that is disipated.
|How do you go uphill easily.
Kneale's answer is it, but there are 2 other ways other than side stepping and herring bone. One is to skate (only possible on a slight incline) and the other is to use a lift of some sort (the easiest).
|How do you increase your skiing speed (for both crosscountry and downhill).
For both cross country and alpine, moving across a flat or a very slight incline, to increase speed there are several things that allow you to accelerate. One or both can be done. One is to use the ski poles to push with and the other is to skate (much like on ice skates). A third option is the wax that you use. A qlide wax will increase acceleration along with an areodynamic body position (a tuck) and areodynamic clothing (speed suit).
It is good to know your abilities and terrain before tucking a slope for the reasons Kneale mentioned.