How to specify different colors with ggplot

You do this in two steps:

First, you define the groups that should have different colours; either by adding another column to the data frame or inside aes. I’ll use aes here:

aes(wt, mpg, color = cut(mpg, breaks = c(0, 20, 25, Inf)))

Secondly, by specifying a manual colour or fill scale:

scale_color_manual(values = c('blue', 'green', 'red'),
                   limits = c('(0,20]', '(20,25]', '(25,Inf]'))

This specifies which colours to use (values) and which labels to assign them to (limits); these are the names of the grouping generated by cut.

Taken together:

ggplot(mtcars) +
    aes(wt, mpg, color = cut(mpg, breaks = c(0, 20, 25, Inf))) +
    geom_point(size = 4) +
    scale_color_manual(values = c('blue', 'green', 'red'),
                       limits = c('(0,20]', '(20,25]', '(25,Inf]'))

You can improve the legend title by adding the grouping as a separate column to your data, or by providing a guides function call:

guides(color = guide_legend(title = 'mpg range'))

Sure it can, although this type of work if probably best suited to working with your data frame before ggplot(). You could use ifelse() like this:

library(ggplot2)

p <- ggplot(mtcars, aes(wt, mpg))
p + geom_point(size = 4, 
               aes(color = ifelse(mpg > 25, "> 25", 
                                  ifelse(mpg > 20, "20-25", "< 20")))) +
  scale_color_manual(values = c("> 25" = "red", "< 20" = "blue", "20-25" = "green"),
                     name = "MPG"  )

You don't need to call guides() to create a title you can pass it to the name = .. argument in scale_color_manual()