Download this:
http://rapidshare.com/files/176334055/The_Ultimate_Fallout_Installation.rar
And install it like this:
1) Install Fallout 1 from GOG.com
2) Find and install "Fallout_1_TeamX_Patch_ENG_1.2w" (either via nma or just google)
3) Install "f1child_patch" (again, nma)
4) Install "fallup13" - this is the TeamX patch 1.3.4 (nma)
5) Install "f1npcmod" from TeamX (again, nma)
6) Install "sfall1" (from http://timeslip.chorrol.com/sfall.html)
7) Install "Fallout1_High_Resolution_Patch_v1.3" (nma)
8) Open f1_res and set AUTO_SCRN_SIZE = 0, then your desired resolution (I use 800*600, anything above is just too darn small for my taste), then if you want, change the way ingame movies work, either fullscreen or not....up to you.Same with movie subtitles.
It should work without any problems - I finished the game with zero bugs or problems with this procedure.

There is a newer version of that mod here:
http://nma-fallout.com/forum/dload.php?action=file&file_id=1135
There is a readme in the .rar file.
Also, if you do Paul_cz's method, you don't need to install the TeamX 1.2w patch, the GoG version is already 1.2, so you can go straight to the fallup13 patch.
I want to play through it the first time as the game was originally intended, so I'm just using the fallup13 and the f1child_pack. I'll experiment with game changing mods after I finish it and Fallout 2.