It depends entirely on what I'm making.
If I'm making a large bowl from a crotch of a tree, I rarely draw anything (except some circles with compasses to find the right center) until I've turned it round, remove chain saw marks and have a look at the grain and the general shape of what's left, then I take it off, set it down on a table and try to make an accurate sketch and decide what curvature and foot will look best. Afternoon light and a beer help a lot at this point. I find this sketching process to be the crucial difference between a truly elegant and beautiful piece and a somewhat klunky looking present for someone that will appreciate it.
If it has some great surface features I want to include in a natural edge, I will often spend a lot of time working out where the center and bottom plane should be, and after doing a bunch of geometric constructions directly on the log, I'll mount it at what I think is the correct center with a few screws, then turning it by hand, see if the features on the natural edg lie where I want. if not, I make careful measurements and re-set the face plate, sometimes with wedges if the angle of the base plane is off. This can go on a couple times if it's really hard.
For example this one:
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was a monster piece of olive that has a completely continuous natural edge, even continuous with the hole in the surface, and that took a couple mountings to get it right (I first glued a large flat piece of ash onto the bottom so I could turn the off center bowls inside). It was hard because of the irregular shape and you can see where there was an unavoidable chain saw cut which I planed flat (luckily the natural edge was still continuous around the outside, though it narrows down to about 1/16" wide at the lower right edge). Some others, such as these Frankenstein bowls
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I will first choose the center for a natural edge, turn it round, then spend a lot of time sketching before I add pieces of wood to span gaps. Adding the dovetail joints, I don't usually draw, it's more of a process of examining the grain and seeing what will be sound enough to take the dovetail and just will give a pleasing look. These are not drawn quite as much when I add the extra wood when I join two burls together. Instead I just use my hands to feel in empty space where the already turned surface will be in the pieces of wood will end up, holding them together by hand and turning the lathe by hand to see where the second burl will get cut. The multi axis bowls and vases I will draw in much greater detail before I turn, even down to which centers will be turned in what order and which cuts will be done now or later, after mounting on other centers and then coming back again to the original center. There is sometimes a lot of jig building that goes on for them and wedges and more geometric constructions in 3D with the wood propped up on the bench, using a large square (or two) to mark where different centers ought to be to get the features I want. If it's a matched set of things, I have a detailed drawing with some specific dimensions that have to match.