Burning Folder to DVD
I'm assuming a "G-Drive" is an external (USB or Firewire) hard disk, right? If it's some online solution (Google etc.) you'll probably need to copy the files to your local disk first (e.g. to your desktop). Downloading speed would never match your DVD burner speed anyway.

The normal procedure of burning files to CD or DVD is extremely simple. You create a "burn folder" much like you create a "project" in Windows burning software, only the paradigm is far simpler, you do not need to learn (or buy) another application just to burn files to disk, everything is in Finder. Burn folders are just normal folder except for that they 


only contain aliases (links) to the files that are to be burnt (just like your "burn project" in Windows)
contain some extra attributes for the disk like burn speed, volume label and so on
are treated specially by OS X when it detects a burnable disk is inserted
automatically calculate the space required and warn if the files don't fit


Try not to think so much, it helps losing all the complicated workarounds you were used to in Windows ... :-)

Do this:


Open Finder, in its menu select File > New burn folder
Drag all items to be burned into this folder. Finder will create aliases, not copies. If you only have one folder to burn, drag its contents into the burn folder. Rename the burn folder how you want your disk to be named.
In Finder, open the burn folder. You'll see a button at the top labeled "Burn". Click.
Insert DVD, follow instructions.


Alternatively, you can also just insert the DVD and OS X will ask what to do with the empty disk: if you select "Open in Finder", it will automatically create a burn folder for you and show it in the sidebar. Drag items into it, select "burn" like above and follow instructions.

Here's a tutorial with screenshots (showing outdated OS X versions, but visually, not much changed since then): http://www.macforbeginners.com/page.php?id=187

If this procedure doesn't work as expected, maybe you can share some screenshots showing what exactly went wrong.