The data are a series of dates and times.
date time
2010-01-01 09:04:43
2010-01-01 10:53:59
2010-01-01 10:57:18
2010-01-01 10:59:30
2010-01-01 11:00:44
…
I'd start by reading about as.POSIXct, strptime, strftime, and difftime. These and related functions should allow you to extract the desired subsets of your data. The formatting is a little tricky, so play with the examples in the help files.
And, once your dates are converted to a POSIX class, as.numeric() will convert them all to numeric values, hence easy to sort, plot, etc.
Edit: Andre's suggestion to play w/ ggplot to simplify your axis specifications is a good one.