How do we compute the ring of integers in a finite extension of $\mathbb{Q}_p$? Say, for example, in $\mathbb{Q}_p(i)$. Over $\mathbb{Q}$ we would guess $\mathbb{Z}[i]$, compute the discriminant of this $\mathbb{Z}$ module and look for squares dividing it. But squares in $\mathbb{Z}_p$ are slightly more complicated than in $\mathbb{Z}$.
Is there some easy way to see the ramification degree / the degree of the residue field extension? If this were the case then it would be very easy to write down the valuation on the extension.