The Sydney Morning Herlad's Steve Manfredi gives his views on the different methods for curing olives in this article. According to Manfredi,
"Lye-cured and ash-cured olives are best avoided. This rather harsh treatment softens the flesh and strips the olive of most of its flavour. This type of olive is uniformly jet black and lacks any true olive flavour.
Brine curing is another matter. There, the olives - almost always green - are soaked in a saltwater bath for up to six months. The bitterness is leached out slowly but the flavour is miraculously preserved. Brine-cured olives usually have a smooth, shiny skin and can show differing varietal characteristics.
For most black olives, and for green olives where a crunchier texture is desired, dry salt-curing is the go. The olives are layered with coarse salt in roughly a two-to-one ratio. Every three days they are mixed through the salt and after two months they're washed, dried and preserved in olive oil and aromatic herbs."
He also provides a nice recipe for chicken with olives.