Even before the outbreak of the first World War, Ravel was planning to write a "French suite" for piano, using 18th century models. In the event it was not until 1917 that he was able to complete it, and by then it had taken on the form not just of an hommage to his musical predecessors but of a tribute to friends who had died in service during the war. The piano version is in six movements:
dedicated to Jacques Charlot
dedicated to Jean Cruppi
dedicated to Gabriel Deluc
dedicated to Pierre & Pascal Gaudin
dedicated to Jean Dreyfus
dedicated to Joseph de Marliave
The piano version was given its first performance in 1919 by Marguerite Long. (See Long , pp.93-97).
A performance of the Toccata is included among the piano roll recordings which Ravel made in 1922.
In 1919 Ravel orchestrated four of the movements (Prélude, Forlane, Menuet, Rigaudon - in that order). This was first performed in February 1920 in Paris by the orchestre Pasdeloup conducted by Rhené-Baton. [A different orchestration, or "transcription pour petit orchestre" with piano-conductor, was made by Roger Branga (a pseudonym of Lucien Garban) and was published by Durand in 1924. This comprised only three of the movements - Prélude, Menuet, Rigaudon.]
A discussion of the musical links between Ravel and Couperin can be found in "History and homage" by Barbara L. Kelly (in Mawer  pp.19-22).
Copies of the original piano score (1918) and orchestral score (1919) can be downloaded, within permitted jurisdictions, from the IMSLP/Petrucci Music Library. A new edition of the piano score by Roger Nichols was published in 1995: Maurice Ravel, Le Tombeau de Couperin: solo piano; Urtext edition. London, Edition Peters, c.1995. 38 pages.