If you'd like to see the machine in operation, here's a video by Ron Covell, a masterfully skilled sheet metal craftsman: https://www.youtube.com/watch?v=omRlIBONJAM
A craftsman can carefully shape the metal to whatever shape was desired. But accurate? Who said anything about accurate? It's likely that everyone's paneling was of slightly different curvatures. They'd machine the mounting holes after the fact, so those would all match and be replaceable, but why would anyone care (how would anyone know?) if the curvature of the fender was a few millimeters different from another fender?
Sometimes they had wooden shape templates... roll the part between the wheels until it seems ok, put it on the template, see where it's not quite right, back on the rollers, back on the template, back on the rollers, until the part was accurate enough.
There are some luxury motor car brands that make a point of still using the panel beating (aka panel patting) techniques for their production. It adds months to the production time of highly skilled, and thus very expensive, panel beaters... but that's the price of oppulence.
Using them is an art.
This can then be translated to a series of full-scale wooden templates, either interlocking 2D sections, or 3D carved from solid. Alternatively, small diameter metal rods can be bent and welded together for a same purpose. Either technique allows a craftsperson to combine precisely formed 2D curves into a 3D shape. Small design changes would also be made at this stage, usually by eye rather than to a particular measurement. This full-scale reference model is called a body buck or in Italian "manichino."
Once you have the complete buck, craftspeople would shape flat aluminum panels into to fit on various sections of the buck. The craftsperson works iteratively until the shape is right, using tools such as an English wheels, bending brakes, mallets and sandbags as well as cutting tools like shears and hole punches.
Once the shape of each individual panel is correct, they are fastened to the car chassis by welding or a mechanical fastener like a screw. The appearance and surface of the body is still quite rough at this point, so there is an extensive manual finishing process before paint is applied. Panel gaps are adjusted, bulges and dents are tapped out with hammers, lots of sanding. Soft filler materials are applied to fill and smooth the body surface- we use "Bondo" for this now but back then they used a lot of lead. The "accurate" appearance of a final painted car body comes from this hand finishing process. However, accurate is a bit of a misonmer as even though the body may look smooth and shiny there are often a lot of geometrical imperfections and asymmetries. For example, headlights in slightly different positions, replacement windshields won't fit etc. For certain models, you can even use predictable "imperfections" in the bodywork to determine whether the body was replaced or majorly repaired at some later date.
This technique was in wide use in Italy (probably other places too, but idk) through the mid-1960s, at which time modern stamping processes became able to cheaply mass produce panels with much less manual labor. As this process is so labor and skill intensive, it's now a specialty. Even among auto body repair professionals, it's uncommon to find someone with the skill to shape large panels from scratch to a high standard.
If you're interested in this type of stuff, there's a great youtube channel called "cbrwatahiki"[0] where a guy uses manual techniques to reproduce aluminum car bodies in his garage. Language is Japanese but it's still possible to watch and learn a lot if you can't understand. While his methods are not quite the same as what a 1930s-50s era production shop would use, it still shows a lot of what is involved to fabricate a body based on a pattern.
[0] https://www.youtube.com/channel/UCZjqr9ScOlWSkcnTK_mLiSA