Make sure all the tiles are producing shields and commerce, otherwise the GA might go by unnoticed... This means roading tiles which are not on a river, it may even mean mining the grasslands that have been irrigated.
I am not particularly happy with settlers running around during the GA because that means they aren't working any tiles. But I realise this is the time to get the territory expanded so I usually build them anyway. Early GA's usually have a bigger impact on history than late GA's, because they can help you get ahead of the AI in such way that you 'll never lose your place. But the less cities you have, the less impact the GA will make.
GA's during wars are not a bad thing at all. You can crank out military units like they cost nothing, and because you usually have money to burn, can buy dozens of temples, barracks etc. in newly captured towns.
The best use of GA's is building wonders though in my opinion. There have times where I built all Middle Age wonders thanks to a well timed GA (early Middle Ages like superslug said or slightly later).
The big DO-NOT is having anarchy or despotism during the Golden Age, because of their tile penalty. If you start the GA during despotism, chage governemt asap tho so you get at least a few turns in monarchy or republic.