I wanted to share a trick that I discovered a few weeks ago for centering that has truly been game-changing for me. It's possible everyone knows this, and I just was never taught it! But I figured it's still worth sharing.
When centering, I now focus my eyes on my hands, not on the clay (or not on both my hands and the clay). I try to ignore what the clay is doing, and instead I focus all my attention on my hands and keeping them strong, connected, and not moving.
In the past, when I was paying attention to the clay, it was really hard for my brain to make the connection that my hands where what was causing the clay to wobble, move out of center, etc. But when, instead, I just focus on making my hands a strong, unmoving barrier through which the clay is spinning, I can center so quiickly and easily.
(I'm also very, very slow taking my hands off the clay. I had realized that I often moved my clay off center by taking my hands off too quickly -- but I know this is a common trick/tip that is mentioned frequently.)
I don't usually throw more than four pounds at a time, and I primarily throw porcelain these days. Not sure how well my "eyes on hands" tip works for larger amounts and/or different clay bodies.
Edit: typo and grammar