Manin's ICM talk at Nice (1970) might be a good place to start.
If you read French, an elementary introduction to the local-to-global principle and to the Manin obstruction can be found on David Harari's homepage. This article also appeared in the Gazette des Mathématiciens (Janvier 2006).
A detailed treatment can be found in the book
MR1845760 (2002d:14032) Skorobogatov (Alexei), Torsors and rational points. Cambridge Tracts in Mathematics, 144. Cambridge University Press, Cambridge, 2001. viii+187 pp.
