Paper Model add-on
Paper Model add-on takes care of everything automatically and you do not need to do anything unusual for this to work. You simply need to disable Automatic Scale and leave the default value of 1 to make it 1:1 size.
The addon saves a PDF file in the chosen standard size that you can then print. The file has exact standard dimensions so if its A4 for example, it's 2480x3508px or 209.97x297.01mm in 300DPI resolution. When printing, you have to make sure printer prints at actual size without fitting content to page, because it would shrink the document to fit within margins that are needed for most printers.
It looks different in various printing dialogs of various different software, but you need to look for some scale setting and set it to actual or 100% instead of Fit to Page. If I wanted to print a PDF file that I opened in Chrome browser, that would look like this:
Printing scene size
If you wanted to print something 1:1 size as in your 3d scene, that's also possible. For real scale to make sense in a render, you need an orthographic camera, and set it's scale to the scale of the bigger dimension of your render resolution. So let's say I want to print A4 size. I need to set render resolution to it's pixel dimensions at my desired DPI resolution and set the camera scale to 297.01 mm:
The resolution of rendered image is 72 DPI by default so one also needs to fix that in some other program like Photoshop before printing since the dimensions in pixels are for 300DPI.