Here’s the centering tips I remember from last week:

If you have trouble with clay drying out too much as you’re wedging, wet the surface slightly with a sponge and then wait for it to dry, then wedge. 

Make a teardrop shape from your lump of clay and jam the point on the center of the wheel. It doesn’t have to be thrown. Whack it into the center and whack it down firmly in place. 

Press down the edge of the lump all around, making a “ruffly skirt” sealed to the wheel. Wet a finger and press between the lump and the edge of the skirt, rotating the wheel to seal. 

After this point, never touch clay unless wheel is in motion. 
Wheel should turn in the direction dominant hand points. 

No need to wedge elbows any particular place, but keep hands as still as possible on clay as wheel rotates to make it even more centered. Patience is key. “Let the wheel do the work.”

Coning is important, it forces air bubbles into the center so they go away as you open up. 
Use a finger to make a groove at the bottom of the lump. Pinkies go here; alternate pulling the clay upward and pressing it together until you make a tall cone. 

Point of cone goes in palm of dominant hand, whose fingers go down the side of the cone. Supporting hand palm touches clay and fingers support dominant hand fingers. 
Dominant hand pulls cone down gently and wheel pulls the clay in to center. “Let the wheel do the work.”  There’s a little subtlety of positioning  to this I find it hard to describe verbally. 

Now you can make things!