To send resources to your great work, zoom out to the region view and click on the great work site - this will show you a status screen detailing each of the resources required to build the great work and the quantity of each resource that has already been supplied.
To enable your city to send resources to the great work, you will see on this screen that underneath each resource is a 'power button' (it looks the same as the power buttons to disable buildings). Turn this on and you will start sending resources to your great work site.
Every city in the region that is within range of the great work site will have their own controls for sending resources to the great work site, allowing for a group of people to participate in building a great work, with each potentially providing a different type of resource.
The frequency of delivery of the resources to the Great Work depends entirely on the availability of the resource at the Trade Depot(s) and the number of delivery trucks available to take it there.
As of patched version 10.3, the Trade Depots (resource sink) suffer from a bug that allows the delivery trucks to park at an alternate resource source as well as drive out of the city to an unknown destination and not return. Therefore, if your delivery truck garages at your Trade Depot are empty (no trucks parked inside), then you should bulldoze the empty garages, rebuild them and they will begin delivering from the Trade Depot again.