Help with a proof using the pumping lemma

Question

I am confused with even starting the proof. I understand the pumping lemma:

Let A be a language over $\Sigma$. If A is regular, then there exists $p > 0$ (pumping length) such that $∀s∈A$, if $|s|≥p$, then there exists $x,y,z∈ \Sigma^*$ such that $s = xyz$ and:

1. $|y|>0$
2. $|xy|≤p $
3. $∀i∈ℕ x(y^i)z∈A$

What I am confused about is how does a computational trace end in a repeated state and have a length at most of length $|Q|$? How can I come about proving the statement using the pumping lemma?