Controlling simple output with a button and a relay
When the button is pressed, it allows electricity to flow through it, between its two connections.
You can wire the relay's N.O. and C. (not N.C.) connections in parallel with the button (i.e. wire one to each terminal of the button). It doesn't matter which one goes to which wire on the button. When the relay is activated, electricity can flow between N.O. and C. just like a switch.
So electricity can either flow through the button, or around the button and through the relay. Or both at once, if you happen to press the button and activate the relay at the same time.

Just to help your understanding of circuits a bit (you garage door won't actually be wired like this): if the button worked the other way - if it blocked the flow of electricity when you pressed it - how could you wire the relay?
In that case you could wire the N.C. and C. connections of the relay in series with the button, so the electricity has to flow through both. Then, pressing the button would block the flow of electricity, and activating the relay would also block the flow of electricity, since the relay only allows electricity to flow between C. and N.C. when it's not activated.

By the way, when I talk about &quot;the flow of electricity&quot;, it's not the electricity going to the garage door motor - it's a separate, very small trickle of electricity, which the control circuit tries to put out in order to sense whether the button is pressed.