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There is a pretty good account of how this works in Karl Schwede's paper:

MR2182775 (2006j:14003)

Karl Schwede, Gluing schemes and a scheme without closed points.

Recent progress in arithmetic and algebraic geometry, 157–172, Contemp. Math., 386, Amer. Math. Soc., Providence, RI, 2005

See also this paper:

MR2044495 (2005a:13016)

Ferrand, Daniel Conducteur, descente et pincement.

Bull. Soc. Math. France 131 (2003), no. 4, 553–585.

show/hide this revision's text 1

There is a pretty good account of how this works in Karl Schwede's paper:

MR2182775 (2006j:14003)

Karl Schwede, Gluing schemes and a scheme without closed points.

Recent progress in arithmetic and algebraic geometry, 157–172, Contemp. Math., 386, Amer. Math. Soc., Providence, RI, 2005