Find the day of a week

Look up ?strftime:

%A Full weekday name in the current locale

df$day = strftime(df$date,'%A')

Use the lubridate package and function wday:

library(lubridate)
df$date <- as.Date(df$date)
wday(df$date, label=TRUE)
[1] Wed   Wed   Thurs
Levels: Sun < Mon < Tues < Wed < Thurs < Fri < Sat

df = data.frame(date=c("2012-02-01", "2012-02-01", "2012-02-02")) 
df$day <- weekdays(as.Date(df$date))
df
##         date       day
## 1 2012-02-01 Wednesday
## 2 2012-02-01 Wednesday
## 3 2012-02-02  Thursday

Edit: Just to show another way...

The wday component of a POSIXlt object is the numeric weekday (0-6 starting on Sunday).

as.POSIXlt(df$date)$wday
## [1] 3 3 4

which you could use to subset a character vector of weekday names

c("Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", 
    "Friday", "Saturday")[as.POSIXlt(df$date)$wday + 1]
## [1] "Wednesday" "Wednesday" "Thursday"