What do you use to design a new piece of software?

In the meantime, I simply use pen, paper and ring-binder. I tend to write with the granularity of a single page. That is, decompose functionality, etc, so that resulting sketches, etc fit on a single page. I don't fear mostly blank pages. Easier to find stuff as I flip through the pages.

Once I get down to the granularity of a class, function, module, I implement it and mark the page as done with a date. Any key design decisions, discoveries, etc are transcribed into the comments of that source file.

I also use GraphViz to generate some dependency diagrams. SVG files are easy to view with any HTML browser.

Heirarchal notes let you organize however you want, you can make your own little wiki to handle the zooming.

I also am very much considering getting some kind of digital drawing device, like a Boogie Board with the smart pen, or else waiting till there's an affordable stylus phone that I like(The Moto Stylus is the only recent cheap one and that lacks wireless charging).

But for now I primarily rely on text for everything, until I'm ready to move into CAD or code or whatever I'm doing.

Iterative designs, rather than full top-down where everything is figured out in advance, have proven to be more flexible and faster to implement. This is part of the "worse is better" philosophy of software design.

As for UI/UX, give Figma a try. It's powerful, supports all kinds of design work (workshops, sketching, prototypes, presentations) and has a generous free plan.

Not appropriate for everything, but for most things I do, can't be beat.

I also wrote my own tool to design/spec/test such designs.