How can I move the y axis label from the left to the right of the plot area and the x-axis label from below to above the plot area in the following graph? Thanks
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By default R will plot the x-axis below the plot area and the y-axis to the left of it. You can change this behaviour in this way:
plot(1:100, cumsum(rnorm(100)), type="l", axes=FALSE) # Do not plot any axes
axis(3) # Draw the x-axis above the plot area
axis(4) # Draw the y-axis to the right of the plot area
box()

To also move the labels you set ann=FALSE or xlab="", ylab="" and add them afterwards with mtext, where side=1 is bottom, 2 is left, 3 is top, 4 is right. line controls the distance from the plot area.
plot(1:100, cumsum(rnorm(100)), type="l", axes=FALSE, ann=FALSE)
axis(3)
box()
mtext("Top axis", side=3, line=3)

Use the mgp parameter to control these details, either before the call to plot, like this
par(mgp=c(axis.title.position, axis.label.position, axis.line.position))
or in the plot command itself, like this
plot(1:100, cumsum(rnorm(100)), type="l", mgp=c(2,1,.5), las=1)

Also note the las parameter that turns all tick labels horisontal, which makes them easier to read.