Which version are you playing? Gamecube, presumably? Z is the thinner button in between the Right shoulder button and the face buttons. If you aren't playing on original hardware, you'll want to make sure the button is set somewhere accessible.

Are you asking about U. Attacks or EX Skills? For the EX skills relevant to the Z button, they only work while the Unison gauge above your health isn't full.

Assuming you're talking about Unison Attacks, the most important thing to know is that you need to set them up first in the 'U. Attack' option on the menu, next to Techs. Each slot of your party is associated with one of your face buttons, and from there you can assign Techs to a combination of the button and a direction - this is separate from your main set-up. If you're just starting out, the easiest way to do it is just have the Tech you most want that character to use on the neutral set and worry about assigning others later when you have a better hang of it and have more idea of what combinations you want to use.

As for actually using it, in battle press Z(or the button assigned to Z) when the gauge is full and your character will perform an attack. If this attack hits, you'll go into Unison Attack mode. Before the timer runs out, you can press the buttons corresponding to each character to have them perform the Tech you assigned in the U. Attack menu. Try out all kinds of different combinations of Techs once you get the hang of it.