Hi Colin,
I am appending a list of references I found useful.
MR0243527 (39 #4848) Mitchell, Barry . Spectral sequences for the layman. Amer. Math. Monthly 76 1969 599--605.
MR1721118 (2000m:55003) McCleary, John . A history of spectral sequences: origins to 1953. History of topology, QA611.A3 H57 1999 631--663, North-Holland, Amsterdam, 1999.
Matthew Greenberg:Spectral sequences http://www.math.mcgill.ca/goren/SeminarOnCohomology/specseq.pdf
Tom Weston:Inflation-Restriction sequence http://www.math.mcgill.ca/goren/SeminarOnCohomology/infres.pdf
http://www.cmi.ac.in/~suman/academic/pranab/node2.html
Romero, Rubio, Sergeraert : Computing Spectral Sequences : http://www-fourier.ujf-grenoble.fr/~sergerar/Papers/Ana-JSC.pdf
David Brown Serre spectral sequences and applications http://math.berkeley.edu/~teichner/Courses/Surveys/DavidBrown.pdfhttp://www.math.wisc.edu/~brownda/math/papers/sss.pdf
