Determine the data types of a data frame's columns

Your best bet to start is to use ?str(). To explore some examples, let's make some data:

set.seed(3221)  # this makes the example exactly reproducible
my.data <- data.frame(y=rnorm(5), 
                      x1=c(1:5), 
                      x2=c(TRUE, TRUE, FALSE, FALSE, FALSE),
                      X3=letters[1:5])

@Wilmer E Henao H's solution is very streamlined:

sapply(my.data, class)
        y        x1        x2        X3 
"numeric" "integer" "logical"  "factor" 

Using str() gets you that information plus extra goodies (such as the levels of your factors and the first few values of each variable):

str(my.data)
'data.frame':  5 obs. of  4 variables:
$ y : num  1.03 1.599 -0.818 0.872 -2.682
$ x1: int  1 2 3 4 5
$ x2: logi  TRUE TRUE FALSE FALSE FALSE
$ X3: Factor w/ 5 levels "a","b","c","d",..: 1 2 3 4 5

@Gavin Simpson's approach is also streamlined, but provides slightly different information than class():

sapply(my.data, typeof)
       y        x1        x2        X3 
"double" "integer" "logical" "integer"

For more information about class, typeof, and the middle child, mode, see this excellent SO thread: A comprehensive survey of the types of things in R. 'mode' and 'class' and 'typeof' are insufficient.

sapply(yourdataframe, class)

Where yourdataframe is the name of the data frame you're using

I would suggest

sapply(foo, typeof)

if you need the actual types of the vectors in the data frame. class() is somewhat of a different beast.

If you don't need to get this information as a vector (i.e. you don't need it to do something else programmatically later), just use str(foo).

In both cases foo would be replaced with the name of your data frame.