Question

What are the oxidation numbers for $Cl{O}^{-}$?

Answer 1

You're dealing with the hypochlorite anion, $Cl{O}^{-}$, so right from the start you know that the oxidation numbers of the atoms that make up the anion must be equal to −1, the overall charge of the ion
This means that you can write
$O{N}_{chlorine}+O{N}_{oxygen}=-1$
Now, oxidation numbers are all about electronegativity. As you know, oxidation numbers are assigned with one concept in mind - that more electronegative atoms will take the bonding electrons from the bond it has with a less electronegative atom.
When oxygen is paired with a less electronegative atom, its oxidation state is always equal to −2.
In this case, oxygen is indeed more electronegative than chlorine, so you can say that
$O{N}_{chlorine}+(-2)=-1$
This means that you have
$O{N}_{chlorine}=-1+2=+1$
The oxidation numbers for the atoms that make up the ion are
$\stackrel{+1}{Cl}\stackrel{-2}{O}$