Hi Michael,
In general, "zu" is always combined with infinitive verbs (zu gehen, and not zu gehst).
The use of it is almost the same like in English...however with some exceptions where you don't need "zu", as it has already been correctly explained above.
Your example:
The second sentence provides additional information or completes the idea of the main sentence, what means that we need "zu" for the last verb in this sentence.
First: Ich möchte die Gelegenheit nutzen, (like a opening,main sentence)
second: es zu sehen.
Some other examples:
Wir sind hier, um euch zu sehen= We're here to see you.
Sie verliess das Geschäft, ohne zu bezahlen= She left the store without paying.
Sandy versucht zu tanzen= Sandy tries to dance.
As you can see, zu+ infinitive verb starts often with these three typical prepositions as well:
um= in order
Wir sind hier, um euch zu sehen= We're here (in order) to see you.
ohne= without
Sie verliess das Geschäft, ohne zu bezahlen= She left the store (without) paying.
anstatt= instead
Er benutzt Mundwasser,anstatt sich die Zähne zu putzen=
He uses mouthwash (instead) of brushing his teeth.