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.
gaming.stackexchange.com/users/52800/kalina
Yeah you definitly have to "use locally" and it takes a while for the flow of transfer to the great work, obviously dont sent more than your budget will allow since you'll be taking a hit on export profit.
gaming.stackexchange.com/users/43917/user43917
Since you can build more than one Trade depot, you can assign one for local use to send to the great work area while assign the other one to export some of your product, but you have to make sure you produce enough to keep up with the great work area.
gaming.stackexchange.com/users/47396/The_Night_Site
How do I send resources to a “Great Work”?
kalina has done a great job explaining this in general.
Local, import or export?
Since no one has tested or elaborated on this I will explain a little further:
Does anyone know if I have to set the trade settings to "Use locally" instead of "Export" to make them send the resources to the project?
If you set the "Global market deliveries" to export trucks will not deliver resources to the Great Works site, but rather leave the city and give you profit for the resources.
If you set the "Global market deliveries" to import trucks will deliver the imported resources to the Great Works site.
If you set the "Global market deliveries" to local trucks will deliver the resources to the Great Works site.
How long does it take to send those resources?
This is hard to say.
It will depend on how many Trade depo/ports you have, how many trucks those have and the traffic.
The easiest way to find out is to measure the time it will take for one truck to deliver a certain quantity.
I tested this (today) on the latest updated version of SimCity.
gaming.stackexchange.com/users/133645/Arete
The fastest way is to put all of your trade ports to import great works resources you need.
gaming.stackexchange.com/users/46071/dirtypignap
I have started building the Arcology project, and I'm producing metal and alloy myself. Normally I export these products to earn money, but does anyone know if I have to set the trade settings to "Use locally" instead of "Export" to make them send the resources to the project?  How long does it take to send those resources? I'm producing around 100kg metal a day, and 2,8t is needed. So it should go pretty fast huh?  Thanks!
How do I send resources to a "Great Work"?
gaming.stackexchange.com
<simcity-2013>
gaming.stackexchange.com/questions/108763
gaming.stackexchange.com/users/43871/Martin
Underneath each resource is a power button. You have to use locally and it takes a while for the trade flow to transfer to the great work. There are few things that can be done in order to provide the demanded resources to a specific place., such as using trade ports to import them.
The community provides information regarding how to send resources to a specific place.