In the Corvallis article *Number Theoretic Background*, here is what John Tate has to say on the local Langlands correspondence for a $p$-adic field $F$:

So, granting a correspondence between irreducible supercuspidal representations of $\operatorname{GL}_n(F)$ and continuous irreducible $n$-dimensional complex representations of the local Weil group $W_F$, the general correspondence between irreducible representations and $\Phi$-semisimple representations of the Weil-Deligne group $W_F'$ should follow.

I understand the (statements of the) Bernstein-Zelevinsky classification of smooth irreducible representations of $\operatorname{GL}_n(F)$. But how are $\Phi$-semisimple representations of $W_F'$ built out of continuous irreducible representations of $W_F$?