Given a date, how do I find the beginning and end of that week?

Assuming you have a standard work week, let's say you have a variable that represents a date, and you want to find out the first and last day of that week (the preceding Sunday, and the upcoming Saturday). 
 
VBScript 
 

<%      d = "2003-11-01"      response.write dateadd("d", 1 - weekday(d), d)      response.write "<P>"      response.write dateadd("d", 7 - weekday(d), d)  %>

 
T-SQL 
 

DECLARE @d SMALLDATETIME  SET @d = '2003-11-01'  SELECT DATEADD(DAY, 1-DATEPART(dw, @d), @d)  SELECT DATEADD(DAY, 7-DATEPART(dw, @d), @d)

 

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If you don't have a standard week (e.g. day 1 = Monday), you could just adjust the numbers used for the calculations (1 and 7). 
 
If you need to find the start of the *business* week, you can add 1 to the first result and subtract one from the second, for example: 
 

DECLARE @d SMALLDATETIME  SET @d = '2003-11-02'  SELECT DATEADD(DAY, 2-DATEPART(dw, @d), @d)  SELECT DATEADD(DAY, 6-DATEPART(dw, @d), @d)

 
However, your calculations might not be so simple, because this obviously doesn't take into account holidays and other interruptions in a typical work week. See Article #2453 for a demonstration of the use of a calendar table to help count business days.