Many folks are unaware that potters not only throw a cylinder on the wheel but we also let it dry to a certain point, flip it, and then carve the "shoulders" and the foot ring!
One of the biggest struggles is in the timing; you must babysit or monitor the piece until it is leather hard. Leather hard is a potter's term for the moisture level of the pot and it basically means enough water has evaporated to the point where you can touch the pot without leaving fingerprints. If you were to drop the piece it would tear and buckle but it wouldn't smash into nothing and it wouldn't shatter, if it were bone dry. We can also use a cheese analogy here! Carving into a hard block of aged cheddar (aka leather hard) will generate crisper lines than carving into a soft gouda.
At Slowfire, we teach our students to monitor their work and then flip it upside on the wheel and carve it with an assortment of carving tools. Each potter has their favorite tools so we provide lots of options for our students to learn what works best for them! I love sharp loop tools myself from Diamond Core whereas others prefer the Mudtool two sided black tool.
Trimming on the wheel is all about removing weight and bulk from a thrown cylinder and revealing an elegant foot. It takes time and practice to learn to trim effectively!
Here are some images of our students learning to trim. Most of these are process pictures but please note Arwa with her gorgeous trimmed bowl.
Please check out my Slowfire Youtube channel where I cover trimming the rim of a cylinder. Youtube link at the very bottom!