DISCLAIMER: I am not a pottery teacher, so if I happen to do something ax*backwards, I can only say it works for me.
I spend maybe more time than I need to trimming. Here's my process (since I don't have a griffin grip like a production potter would.)
First center it on the wheel...set it almost in the middle, turn the wheel slowly, and hold something steady to find where it's off-center...then tap it away from that point until it it truly in the center.
Then attach the pot to the wheel with little blobs of wetter clay. The pot being trimmed is best in a leather hard stage where the top edge (against the wheel head) won't be easily bent out of shape any more.
I try to remember the round bowl shape on the inside (no flat bottoms anymore inside) and I have almost reached the point where the lump on the inner side of a beginning potter's bowl is missing.
The finish trimmed bowl has a much smaller bottom than the original one I started with.
I know a lot of potters prefer a bigger trimming tool. You can see by the size of my shavings that I'm more hesitant to take off a lot of clay at once. But it goes pretty fast.