A long long time ago when I only had a small handful of resistors with values dependent on whatever was in equipment someone else threw away, I experimented with making my own. You'll need very different technologies for making really low and really high values, but let's stick to the more common midrange values.
What worked the best for stuff I had around was a #1 pencil trace on a piece of paper. #1 pencils were occasionally used for tests that were scored by a machine. One time after taking such a test I managed to hold on to the pencil. To make a resistor or bunch of resistors, make traces on a piece of paper, then drive small brass tacks thru the paper at the ends of the traces thru a piece of wood underneath. You can solder straight to the tops of the tacks. By changing the length, width, and amount of pencil material, you can adjust the resistance over a suprisingly wide range.
When I said this was the best method I found, that doesn't mean it was all that good. The biggest problem is these resistors would drift a large amount. Just a tiny touch to the pencil trace could change the resistance significantly. I don't see this working out well for a potentiometer because something would always be rubbing against the trace. Nowadays there are conductive paints and epoxys, but these are expensive. You can probably make a sortof reasonable pot with some effort, but it won't compete in quality and cost with a commercial pot, even if you value your time at 0.
Making low value pots shouldn't be too hard because you can use something that conducts reliably, like a piece of wire or coiled wire to get more resistance. Anything more than a Ohm or a few Ohms will be more difficult.
One time I made a potentiometer that worked very well, but the purpose wasn't to save money or because real pots were inaccessible, it was to get a voltage-controlled pot. I did this with two LEDs and two CdS photoresistors. The result is rather non-linear, but it worked well enough for my purpose, which was to be able to regulate the amplitude of a oscillator that inherently varied with frequency.
So go ahead and experiment for the fun and learning of it. But, don't kid yourself that you'll be able to make anything as accurate, reliable, and scratch-free as a commercial pot for the same cost.