How to tell CRAN to install package dependencies automatically?

I develop a package in R and when I check and build it in my local computer it works properly. But when I tried it in CRAN, I get a package dependencies error. My package depends on two functions of other packages.

If I list the other packages under the description using Depends or imports, will it be automatically installed with the new package? Or do I need to explicitly invoke the function install.packages("packagename") under the function that I've used the other packages. if this all is wrong, what is the best way to solve package dependencies in R inorder to pass the R CMD check and build test and submit to CRAN?

Thank you.

On your own system, try

install.packages("foo", dependencies=...)

with the dependencies= argument is documented as

dependencies: logical indicating to also install uninstalled packages
      which these packages depend on/link to/import/suggest (and so
      on recursively).  Not used if ‘repos = NULL’.  Can also be a
      character vector, a subset of ‘c("Depends", "Imports",
      "LinkingTo", "Suggests", "Enhances")’.

      Only supported if ‘lib’ is of length one (or missing), so it
      is unambiguous where to install the dependent packages.  If
      this is not the case it is ignored, with a warning.

      The default, ‘NA’, means ‘c("Depends", "Imports",
      "LinkingTo")’.

      ‘TRUE’ means (as from R 2.15.0) to use ‘c("Depends",
      "Imports", "LinkingTo", "Suggests")’ for ‘pkgs’ and
      ‘c("Depends", "Imports", "LinkingTo")’ for added
      dependencies: this installs all the packages needed to run
      ‘pkgs’, their examples, tests and vignettes (if the package
      author specified them correctly).

so you probably want a value TRUE.

In your package, list what is needed in Depends:, see the Writing R Extensions manual which is pretty clear on this.

Another possibility is to select the Install Dependencies checkbox In the R package installer, on the bottom right: