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What is a good and relatively brief overview of good practice for getting valid results from surveys.

I'm particularly interested in something about good survey design and analysis.

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This is unanswerable. There are several components of good survey practice: (1) sample design: the classic designs are covered by Cochran (1977) and Kish (1995) that were recommended by Michael Chernick, but the modern reality of phone and address-based sampling are way more complicated, and these books will tell you nothing about practical aspects; (2) questionnaire design and psychometrics of getting valid answers from people -- a totally unrelated area entrenched in psychology rather than in probability theory; (3) survey management -- the art and science of data collection itself; ... – StasK Jun 19 '12 at 14:34
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(4) survey post-processing, weighting and variance estimation, which is a return to statistics -- again, this is a rather poorly covered topic in terms of existing books. My brief learning of this took about two years of two classes per semester. If you are determined to do a survey on your own, you will likely screw up the first one completely, you will miss a lot of good practices on the second one, and your third one will probably be somewhat usable. As a statistical consultant, I've seen all of that, trust me. – StasK Jun 19 '12 at 14:39

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On the more qualitative side of things in survey methodology, see the books mentioned in https://blogs.rti.org/surveypost/2012/05/15/surveying-on-a-deserted-island-a-bakers-dozen-list-of-resources-to-take-along/. If you are totally new to sampling, Lohr (2009) is a more modern treatment covering additionally some of the aspects of survey data analysis, replicate variance estimation, and some practical aspects, as compared to the somewhat more formal classics mentioned by Michael Chernick.

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I agree with Stask on Lohr's book. – Michael Chernick Jun 19 '12 at 15:09
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I recommend Cochran's Sampling Techniques. It provides the fundamentals and is very clear. Leslie Kish's Survey Sampling is another classic that I can recommend. An advantage of going to amazon is that there are often many user generated book reviews there for the OP to look at. I personally have written a lot of reviews there.
I can think of nothing better than an amazon link for textbook because once you get to the site you have user and publisher reviews that you can read and amazon often provides look ins to the Table of Contents,Preface and excerpts to chapters. You are not going to get a link that will give you a free electronic copy of the book. Now reference articles that fit the bill might be possible to recommend but I think the book recommendations are better references in this case. Perhaps a brief monograph like one of the little green SAGE books would suit the OP but I like these books better.

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Previous answers seem to have well addressed OP's question. However, I will add, for the benefit of future readers, that Thomas Lumley has provided a wealth of information on "complex surveys", which can be loosely characterized as surveys with often thousands to tens of millions or more of observations (perhaps data larger than your machine's memory), often implementing complex sampling methods (e.g. National Health Interview Survey or Nationwide Inpatient Sample).

Lumley has contributed to "complex survey" analysis through his R package survey. See here for a list of presentations about the survey package, and here for a number of very good vignettes on using the survey package.

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