My former crew chief taught me how to fold maps but not doing daily production work and with digital submittals, not much folding happens these days.
I learned to fold print side in first. Then fold the printed side out at the 1/4 fold. Like this: /\/\
I personally use a "hard plastic tint film applicator" as found at Amazon here.
I use the cheap-but-sturdy plastic roller that came with the foil inventory tags that I stick onto new equipment. It doesn't have to be fancy, the idea is to make a tool do the creasing work instead of my hands.
We haven't used maps that require folding for many years. All our engineering plans are 11x17 with very few exceptions. Surveys are recorded and scanned, no need to keep original recorded versions anymore. That said, definitely roll them so the information is on the outside of the roll.