The chronological order of the first of R.A. Salvatore's "Forgotten Realms" series is "The Dark Elf" trilogy, "The Icewind Dale" trilogy and "The Legacy of the Drow" series, with the short story "Dark Mirror" coming between the "Icewind Dale" and "Legacy" books. Publication order reverses the first two series.
The next series in order, chronologically, are "The Paths of Darkness" series, "The Hunter's Blade" trilogy, "The Transitions" trilogy, "The Neverwinter" series and "The Companions Codex" series. The "Codex" series is ongoing, and further books are expected. There is also a single book, "The Sundering," which places between the "Neverwinter" books and the "Codex" novels.
As of May 2015, there are 36 published novels by Salvatore set in the "Forbidden Realms," as well as several short stories in various anthologies. His website, RASalvatore.com, offers links to retailers and lays out the order of the series as well as noting Salvatore's non-"Forbidden Realms" work. Because of the sheer volume of novels, and the fact that work is still ongoing, keeping up-to-date with the author's website is one of the best ways to work out which book to read next. It is also worth noting that many readers prefer the publication order of the "Drizzt Do’Urden" series to the chronological order in terms of character development.