Hi!
Yup, you're right: how to equip items is never explained.
The reason for this is pretty straightforward: you don't have to! :D
The inventory is not interactive, actually: it shows your possessions, that's it.
To be more clear: the slots I highlighted in red are for weapons, the green ones are for persistent item, and the yellow ones are for consumables.
(The round slots at the bottom are for something else, but you'll find out for yourself!)