I am new to gog.com and signed up just to get Fallout, after downloading it i came across problems and haven't been able to get it to play.
my problem is it starts, and when i try to skip past the opening cinematic the colors suddenly get all weird and the picture freezes. The sound seems to keep going but im completely unable to play the game.
So far i've tried nearly everything i've read on here, i've renamed falloutw.exe, i renamed ddrawing.ddl, and then tried deleteing it completely.
I'm not very good with computers, and i don't know how to find out what kind of graphics card i have, i also don't know how to find out how much ram i have as well.
I'm desperate for help.

click on start
right click on my computer
click on properties
on the general tab it will tell you how much ram you have.
from there, click on the hardware tab
click on device manager
then click on the plus next to display adapters
it will show your video card (provided you have drivers installed).
Now as far as troubleshooting this issue, make sure you don't have other programs running in the background, try making sure it's running in a resolution your monitor supports, then if those don't work, try using the resolution patch.

try updating your directx -- you need at least directx 7 for the GOG version of fallout, and directx 9 is recommended.
you can find directx here.
i'd also try updating your video card drivers, just in case. if you have a nvidia card, go ; there's a link to download drivers on the home page. if you have an ati/radeon card, go [url=http://ati.amd.com/support/driver.HTML]here.
if that still doesn't work, i'd try the resolution patch as weclock suggested, found here. read the readme file and follow the instructions to make sure that you are running fallout in a 640x480 compatible resolution.

Have you tried running it in 95/98 Mode?
If you have XP try this :
1. Right Click the Fallout shortcut/.exe icon
2. Chose Properties
3. Click the Compatibility Tab
4. Check the Run in Compatibility Mode box and select 95 or 98
Vista should be about the same process.
I'm not sure if this will even work with GOG games since they optimize them for XP/Vista but it's worth a try.
EDIT:
Check out the question about funky colors in this thread