Question

How are oxidation numbers assigned?

Answer 1

All these compounds?

Explanation:

The oxidation number of oxygen in OXIDES is generally `-II`. The oxidation number of a metal is generally its Group Number; i.e. `"barium"` as a `"Group II"` metal generally has a `II+` oxidation state in its compounds. An element has an oxidation number of `0`; i.e. it is zerovalent; `O_2` gas is zerovalent because it has not reacted with (oxidized) anything. The sum of the oxidation numbers is equal to the charge on the ion; viz. `CO_3^(2-)`, if oxygen is `-II` (and it is!), then `C` has a `IV+` oxidation state.

I am unwilling to assign the other oxidation numbers until you make an attempt.