When you select a unit, their stats appear in the lower left corner. There you have buttons to Disband, Guard, Pass, Rename. If your unit can upgrade, there will also be a button there for upgrading (note you might have to click on a "More actions" to see the Upgrade button, or it might be chopped off and show as "Upgr.." There will be separate buttons for upgrade weapons and upgrade armor. Hovering over the button will show the upgrade cost. Click if you want to upgrade.
That is as I thought it should be, but the button is missing.
EDIT: I think it might be a function of not having an item to upgrade.
Let me expand.
I have a unit called AXE that has an axe, but no armor.
Once armor was researched, I edited the unit type to add armor.
So I was trying to upgrade the existing unit that had no armor to upgrade.
I think that is the issue and if it is there is problem with the upgrade system.
Typically ( in other games that I have seen), upgrading a unit meant you could add new weapons/armor/equipment that the unit did not have originally.
If my understanding of the issue in question is correct, the way FW works is you have to have an upgradable item on the unit to begin with, i.e you can upgrade from leather to steel, but not from nothing to leather.