The most authoritative reference is Valliant, Dever and Kreuter (2013). Practical Tools for Designing and Weighting Survey Samples, and the accompanying PracTools package.
C.f. other answers so far in this thread, the authors are actual practitioners in the survey field, and producing/weighting survey samples is one of the central parts of at least Jill Dever's job. (Rick Valliant had just retired as of 2017, and Frauke Kreuter runs two graduate programs on two different continents at the moment; all three are highly regarded statisticians in the survey world).
My own little piece concerns some terminology in the survey weighting literature: Kolenikov (2016). Is it post-stratification or nonresponse adjustment? -- see also references therein.