Some people make custom lamp shade frames so it must be possible. A lot of people suggest wire coat hangers but I think they're too flimsy. It has to be rather sturdy.
What materials you use depends on the design of the lamp shade you want to make – is it a hanging ceiling lamp, a desk lamp, etc. How sturdy the frame needs to be depends on what material it is supposed to support (paper, wood, glass, plastic, etc.) For example, if you are making a paper lamp shade, then the coat hanger wire should be fine (like in those paper lantern lamp shades). If it needs to support glass or other heavy material, then you may need stronger wire, or whatever you can make a sturdier frame out of.
(I’ve made a hanging lamp shade out of just skewer sticks and paper, so again, it all depends on what design you have in mind.)
Some craft shops sell the hoops and the special lamp fittings 'hoop with fitting holder' in a wide range of sizes and shapes.
I got them from a small independent craft shop where I live ( the Netherlands) but I am pretty sure you can buy them online now.
To make fabric covered shades you either need the fitting ring, an extra hoop and sturdy (plastic?) material to connect them or a frame which connects the fitting ring to the outer ring or to a series of rings, depending on the size and shapes you want.
Even with a frame you will likely want lining or a plastic or board layer.
You can also solder or weld your frames from metal rings or rods as available in shops near you or online.
It is not needed to use just one kind and thickness of metal, you can mix pre-made parts with easier to bend metal to work up the shape you want.
To connect you can sometimes wrap rather than solder.
What I do is take old lamp shades apart if there is two layers. A layer of thick like poster board sometimes is on bottom. You can always leave it or you can create a new one with poster board. I spray painted the inside of my lamp shades gold or silver and it would just give off a very beautiful glow!
I would re-cover the outside of the thick poster board with the fabric I choose (using the same wire from the original I tore apart) an I know in craft stores another places they have these little clips that is used for stuff like that which comes in very handy when attaching the fabric. I also you spray adhesive on the fabric and the center part of the shade to ensure it would adhere then clip the fabric at the top then do the bottom. I would super glue my fabric at the top and bottom to then cut off the excess fabric. There shouldn't be much if measured properly. Basically trace your lamp shade on the fabric while rolling it a little at a time. Starting an ending at the seam or you can take off the poster board from the original shade to use as a stencil.
Then, for a professional detailed look, cover the top and bottom edges with trim.