For your first bike, copy a bike you already like. Just about every manufacturer publishes the geometry for each model and size, so it’s pretty straightforward to copy.
Once you’ve decided to make something that you can’t buy, BikeCAD is the way to go. It’s a bargain at $500 (Canadian!). That’s under $400 US at the time this was written. BikeCAD has libraries of most commercially available parts, and it will create mitering templates to cut your tubes.
RattleCAD is an open source alternative to BikeCAD. I have used it a couple years ago and I liked how fully featured it was. I found it less user friendly than BikeCAD, but it may have improved in recent versions.
If you already have a favorite CAD software like Solidworks or Fusion360, just use that.
When I made my first frame, I built a spreadsheet based on the Paterek manual that would calculate all of the lengths and miter angles for me. I used this in combination with this tube coping calculator. Tim Paterek published the first edition pdf of his manual on his website, but it seems to be down as of 2020.
For the true retrogrouch, there’s always the option of making a full size drawing on a big piece of paper. This has the benefit of working nicely with the build method of laying out all your parts on top of your 1:1 scale drawing. It’s a lot harder to revise than a CAD model though. If you really must do this, at least make a spreadsheet to do all of your fit calculations. I’ve made a couple full size drawings just for laughs and it’s super satisfying but not when you have to do it over again and again and again. There’s also the option of having a full scale drawing printed. Even in 2019, there are still printing businesses for blueprints, because they’re still used in the construction industry. A sign printing business could potentially do this too. The blueprint businesses will be able to reliably print to scale. Signmakers are more of a gamble. If I were going this route, I’d make some reference features of known size on my drawing so I could quickly check the scale when I received the drawings from the printer.
A couple notes on safety:
Product liability follows you forever. Even if the end user abuses or misuses your product. If you’re going to sell (or even give?) bikes to other humans, you should carry insurance and do the stuff that the insurance company requires you to do. After making a bunch of bikes, I wish I had cut more of them in half once I had ridden them. That’s not because I’m ashamed of them, it’s because my name was painted on the side and now they’re in the hands of who knows who. I’m responsible to those mystery third parties for bikes that I have no control over. Insurance is expensive, around $2000 per year around 2015.
Making your own vehicle is amazing. I encourage it, that’s why I wrote this. Be cautious about what happens with stuff you make, because it could get real expensive.