How long was the journey in 'The Lord of the Rings'?

The quest itself (=from Frodo setting out to the Ring's destruction) took six months. Another seven months passed until the hobbits again came home to the Shire.

Dates: Frodo sets out from Hobbiton on 23rd September 3018 of the Third Age. Frodo leaves the Fellowship on 26th February 3019. The One Ring is destroyed on 25th March 3019. The hobbits reach Bag End on the 3rd November 3019. Additional note: As can be seen with the above dates, 5 of the quest's 6 months are covered in the LotR's first volume (The Fellowship of the Ring); most of that time is spent resting in RivenDELL and Lothlórien. All the events of the volumes The Two Towers and The Return of the King from Frodo leaving the Fellowship to the Ring's destruction take place in just about one month.