Frustratingly, many birds like to sing unseen from dense cover. Both garden warblers and blackcaps, which have confusingly similar songs, usually sing from hidden perches. It is usually best to wait and watch. Once you have pinpointed the singer, it will only be a matter of time before it moves. If, however, it senses your presence, it will either stop singing or simply slip away, probably unseen.
Some species are notoriously elusive.
Nightingales, for example, can be exceedingly difficult to see in Britain, though in southern France or Spain, where they are generally much more common they are more likely to sing from an exposed perch. I have even seen nightingales singing from telephone wires, something they never consider doing in England. The latter is much the best, as you can simply tap in the track number, and instantly find the song or call you want. The recordings are taken from the extensive collection of the British Library National Sound Archive. There are two CDs, featuring 175 of the most commonly heard British birds.