An elderberry will automatically flower every year. Pruning at the wrong time could actually remove the flowers prune in early spring if you need to.

I'd do it in winter around now if the weather's not freezing cold. Remove old wood at ground level, reduce newer shoots by about half, less if you don't mind a larger plant.

I am going to disagree. As they flower in spring, the blooms are carried on wood made last year; by pruning now or in early spring, you will cut away the wood that is going to carry the flowers. I would say prune immediately after the flowers have finished (but leaves some spent flowers if you want elderberries)

I don't disagree with Andrew either, actually - which method you choose does rather depend on which elderberry you're growing in terms of the variety, and how overgrown and mature it is.

Up here they tend to grow wild and are not pruned at all...

I don't prune mine, (self sown) just cut off lower branches that are in the way. Be careful though - I hear that if you cut down an elder tree it annoys the witches!

If I needed to prune one, I would do it right after it bloomed, since the bloom on the tips of last year's growth. Otherwise, make sure that it is getting enough sun, and is getting enough nutrients, to get more consistent bloom.

Ah memories of making elderberry wine! Almost tastes like port...