The Civic has a push/pull button for the handbrake, as shown in the picture below.
It is located below the gear shift and this is how it works:
To release the handbrake, push down on the button. Switch the gear to D (Drive) and off you go!
To engage the handbrake, shift the gear to P (Park) and pull the button up. To be doubly sure, you'll see the same sign on the button lit up on the dashboard.