This code uses a dataset file with population estimates by the US Census Bureau (more info).

tbl <- read.table(file.choose(),header=TRUE,sep=',')
population <- tbl[c("NAME","POPESTIMATE2009","NPOPCHG_2009")]
smallest.state.pop <- min(population$POPESTIMATE2009)
print(population[population$POPESTIMATE2009==smallest.state.pop,])
      NAME POPESTIMATE2009 NPOPCHG_2009
56 Wyoming          544270        11289

This piece of code extracts the data about the smallest state from the data frame.
The first line has reads the data from the CSV file (as explained here).

Picking specific columns out of a data frame

The second line limits the rows to the state name, the population estimate for 2009 and the total population change for 2009.
Let's use the head function to look at what we get:

head(population)
           NAME POPESTIMATE2009 NPOPCHG_2009
1 United States       307006550      2631704
2     Northeast        55283679       223483
3       Midwest        66836911       241314
4         South       113317879      1296857
5          West        71568081       870050
6       Alabama         4708708        31244

Finding the lowest value in a list

First the POPESTIMATE2009 column is selected:

population$POPESTIMATE2009
 [1] 307006550  55283679  66836911 113317879  71568081   4708708    698473
 [8]   6595778   2889450  36961664   5024748   3518288    885122    599657
[...]
[50]   2784572    621760   7882590   6664195   1819777   5654774    544270
[57]   3967288

Then the min function is used to find the minimum:

min(population$POPESTIMATE2009)
[1] 544270

Selecting the row with the lowest population value

You use something like a WHERE clause in data frame indices:

data.frame[condition]
This condition works because it creates an array of booleans depending on whether the field value is a match:

population$POPESTIMATE2009==smallest.state.pop
[1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE

In this case only the second to last row should be selected. We use a comma after the row index because we want all the columns:

population[population$POPESTIMATE2009==smallest.state.pop,]
      NAME POPESTIMATE2009 NPOPCHG_2009
56 Wyoming          544270        11289