Determine 3rd Friday of each month

Given:

• Friday is called "Friday"

• The 3rd Friday of the month will always fall from 15th-21st of the month

  select thedate
  from yourtable
  where datename(weekday, thedate) = 'Friday'
  and datepart(day, thedate)>=15 and datepart(day, thedate)<=21;
  

You could also use weekday with datepart(), but it's more readable with a name IMO. String comparisons will obviously be slower though.

In order to get a language/culture independent answer, you need to account for different weekday names and start of the week.

In Italy, Friday is "Venerdì" and the fisrt day of the week is Monday, not Sunday as in US.

1900-01-01 was a monday, so we can use this information to calculate the weekday in a locale-independent fashion:

WITH dates AS (
    SELECT DATEADD(day, number, GETDATE()) AS theDate
    FROM master.dbo.spt_values
    WHERE type = 'P'
)
SELECT theDate, DATENAME(dw, theDate), DATEPART(dw, theDate)
FROM dates
WHERE DATEDIFF(day, '19000101', theDate) % 7 = 4
    AND DATEPART(day, thedate)>=15 and DATEPART(day, thedate)<=21;

Another way, that uses Phil's answer as a base, and takes care of different setting:

select thedate
from yourtable
where (datepart(weekday, thedate) + @@DATEFIRST - 2) % 7 + 1 = 5   -- 5 -> Friday
  and (datepart(day, thedate) - 1) / 7 + 1 = 3 ;                   -- 3 -> 3rd week

The 5 code (if you want a weekday other than Friday) should be (the same as SET DATEFIRST codes):

1 for Monday
2 for Tuesday
3 for Wednesday
4 for Thursday
5 for Friday
6 for Saturday
7 for Sunday

---

You can also just use a "known good" date to be safe in the face of language settings. For example, if looking for Fridays, check a calendar and see that January 2nd 2015 was a Friday. The first comparison could then be written as:

DATEPART(weekday,thedate) = DATEPART(weekday,'20150102') --Any Friday

See also How to get the Nth weekday of a month by Peter Larsson.