It's really pretty straightforward.
I dig into my recycle bucket where scraps and trimmings are collected and kept moist, and wedge the clay into a spiral cone to mix and realign the particles so that it is ready to throw on the wheel.
I then center a lump of clay on the wheel preparing to throw maybe a handful of teapots at the time. It is called throwing "off the hump". It is fast. A backhandle teapot consists of three thrown parts (body, lid and spout). Here a spout:
Typically, even in the winter climate, these grogged pots will dry in less than a day. They get placed on a wooden board and often covered with plastic to make sure they will be leather-hard for the next day's trimming and assembly. (The clay is porose and will dry quicker than, say, porcelain. If too dry you can forget working on it any more).
The next day the pots have a foot trimmed on them, the lid is trimmed to fit the pot opening and the handles are formed. Holes are pierced for the filter (how many depends on the shape of the spout of course). It is all assembled in a slow-mo process that requires concentration and some eyeballing.... The overriding principle here is "better safe than sorry".