To extract the weekday, month or quarter, or the Julian time (days since some origin), use the weekdays function that extracts parts of a POSIXt or Date Object.
In your case:
dt = data.frame(date=c("2012-02-01", "2012-02-01", "2012-02-02"))
dt$day <- weekdays(as.Date(dt$date))
dt
Output:
date day
1 2012-02-01 Wednesday
2 2012-02-01 Wednesday
3 2012-02-02 Thursday