This is an irregular verb. It follows the conjugation pattern of the verb passear.
Present:
A Ana ziguezagueia pelo trânsito de bicicleta.
Ana zigzags through traffic on her bike.
Preterite:
O Miguel ziguezagueou pela estrada.
Miguel zigzagged down the road.
Conditional:
A Clara ziguezaguearia para evitar obstáculos.
Clara would zigzag to avoid obstacles.