How to change the font size and color of x-axis and y-axis label in a scatterplot with plot function in R?

Look at ?par for the various graphics parameters.

In general cex controls size, col controls colour. If you want to control the colour of a label, the par is col.lab, the colour of the axis annotations col.axis, the colour of the main text, col.main etc. The names are quite intuitive, once you know where to begin.

For example

x <- 1:10
y <- 1:10

plot(x , y,xlab="x axis", ylab="y axis",  pch=19, col.axis = 'blue', col.lab = 'red', cex.axis = 1.5, cex.lab = 2)

If you need to change the colour / style of the surrounding box and axis lines, then look at ?axis or ?box, and you will find that you will be using the same parameter names within calls to box and axis.

You have a lot of control to make things however you wish.

eg

plot(x , y,xlab="x axis", ylab="y axis",  pch=19,  cex.lab = 2, axes = F,col.lab = 'red')
box(col = 'lightblue')
axis(1, col = 'blue', col.axis = 'purple', col.ticks = 'darkred', cex.axis = 1.5, font = 2, family = 'serif')
axis(2, col = 'maroon', col.axis = 'pink', col.ticks = 'limegreen', cex.axis = 0.9, font =3, family = 'mono')

Which is seriously ugly, but shows part of what you can control

To track down the correct parameters you need to go first to ?plot.default, which refers you to ?par and ?axis:

plot(1, 1 ,xlab="x axis", ylab="y axis",  pch=19,
           col.lab="red", cex.lab=1.5,    #  for the xlab and ylab
           col="green")                   #  for the points