You can either do it with a series of tangental angled cuts and blend them with hand graver and files or work out a set of co-ordinates at say 10 or 20 thou intervals which gives the profile in a series of steps and once again blend them in.
I think one of Ramon's early engine build threads shows him using the tangental method.
If you mean a true spinner (as opposed to a spinner nut) you likely have 2 curved surfaces to contend with. The outer for shape, the inner for weight reduction. Starting with round stock in the chuck, probably best to turn the inside surface first plus any kind of lip geometry plus the center hole. Then, flipping the work around using the lip and/or center hole to secure the part, do the outside cone contouring. If you do it reverse (outside contour first) it will be tricky to hold the part without some kind of dedicated fixture. Hopefully the sketch helps visualize. The curves can be approximated with a series of cuts & blended with a file. The internal surface will be trickier to get blending tools in there. Possibly you could approximate the shell with a series of faceted angle cuts since nobody sees the inside. Then you have to cut the propeller slots & some kind of associated back plate, typically with knurled face for the prop.
There may be shortcuts to this process but I haven't seen too many. I've made one before, they are more complex that a solid, profiled 'nut'. And 90% of the aluminum is in the swarf tray.
I would say two things determine how you make an aluminium spinner as you describe.
1) What machinery do have?
2) What is the actual diameter of the spinner?
Prop nut spinners which look like the US Hamilton Standard spinners or the Cox Tee Dee style can be done with form tools in just about any lathe.
Larger sizes (> 19mm diameter) will need approaches as already suggested, there have also been some spinners commercially manufactured that were spun.
Just for fun a couple of weeks ago my race partner and I made 10 spinners on a CNC mill, you just would not be able to tell they had not been done on a lathe. Constant 3axis spiral cutting path. We did not make the capright at the front of the spinner, that was something we had kicking around.
A CNC lathe is best but like me you may not have access to one.