So, the construction process of of medieval armour is going to differ a lot from the way that you make armour today. For one thing, medieval people did not have homogenous rolled steel, though medieval smiths did use plates of steel (they were just less homogenous and thicker than modern sheet steel, and weren't stainless, either). This means the question 'how do I make this armour today' is not exactly a historical question - because we are not medieval people, we are going to make armour in a way that is fairly different form medieval people, even if the goal is to make an end product that is similar to the original. For a 'how to' you may want to look into the extensive literature on reproducing medieval armour produced by enthusiasts and modern armourers - one commonly recommended work is Techniques of Medieval Armour Reproduction: the 14th Century which covers pairs (coats) of plates, among other things.

Unfortunately, without a forge and some skill at shaping steel it is hard to make even brigandines or pairs of plates - even these armours are not just square pieces of metal, but they are shaped to the body to a greater or lesser extend - requiring at the very least cold-working and an extensive use of sheers (for a 15th century style brigandine).

If you want to learn more about the historical arms industry, my user profile has more information. Nickolas Dupras also wrote a Phd thesis that may interest you - I am still reading it, so I can't speak to its conclusions.