You use BiocManager::install() to install new packages, which it looks like you've done in your example. This step only needs to be done once, they will still be installed next time you start R.
However the error you're seeing is because you're trying to install a package that doesn't exist. readDGE() is a function defined by the edgeR package.
Instead you need to load the package in your R session and then run the function. To load a package you need to use the library() command, and then you should be able to execute functions provided by that package. For example, the code below will load the edgeR package, and then run the readDGE() function.
library(edgeR)
x <- readDGE(files, columns = c(1, 3))
but you have omitted the "Setup" commands listed in Section 3.
In a workflow like this, the later commands depend on earlier steps so you can't generally run later commands without running the preceding code first.