I will begin this tutorial assuming you at least have 2 subtracted brushes in your map, a light, textures for inside/outside areas, and that you want to add Rain to your map. Note: you can click the images to see them full-size.BEFORE YOU START: Make sure you have WeatherEffects turned on in your Editor before you try this, as I had to do this my first time as well 
 
Just go to (menu on top) View > Advanced Options > Display and set WeatherEffects to true Just dumping this here, so that the thread gets frontpage on Google.
General protection fault!
History: AActor::SetZone <- Finishing <- ULevelFactory::FactoryCreateText 
<- UUnrealEdEngine::edactPasteSelected <- UUnrealEdEngine::Exec_Edit 
<- UUnrealEdEngine::Exec <- WEditorFrame::OnCommand <- WWindow::WndProc 
<- WWindow::StaticProc <- MessagePump <- MainLoopFirst thing you will want to do is go to 
Actors > xWeatherEffect, and place one in your map.

Next, open the 
Texture Browser and open 
EmitterTextures.utx.

Under the 
MultiFrame group, select the 
FinalBlend RainFB texture.

Next, open the 
properties for the xWeatherEffect, go to 
Display > Skins > click "Add," then click "Use." It should now show a layer with the RainFB texture selected, and you should now see beautiful floating blobs. You've pretty well already won the battle 
(Note: you can use whatever textures you want, and whatever settings you want from this step onwards)
Now, still in the 
Properties window, go to 
xWeatherEffect and change these settings, depending on what weather effect you're using 
(WT_Rain, WT_Snow, WT_Dust). You may copy my settings (as I copied others 

 ) for a general Rain effect.

Finally, to exclude the xWeatherEffect from certain areas: Make a normal 
Volume surrounding the space in which you want no weather (generally somewhere with a roof). Then under the Volume's properties, go to 
Event > Event, Tag and Volume > AssociatedActorTag  and set them to 
NoRain. Then, open the 
xWeatherEffect properties one last time, and go to 
Event > set both Event and Tag to NoRain. 
Make sure the Event, Tag, and AssociatedActorTag of the volume are the same thing, otherwise this won't work. Note: I enhanced the area outside of the volume (where the sky is). The rain is still visible outside the volume, but not on the inside. 