What should be the values of GOPATH and GOROOT?

I'm trying to install doozer like this:

$ goinstall github.com/ha/doozer

I get these errors.

goinstall: os: go/build: package could not be found locally
goinstall: fmt: go/build: package could not be found locally
goinstall: io: go/build: package could not be found locally
goinstall: reflect: go/build: package could not be found locally
goinstall: math: go/build: package could not be found locally
goinstall: rand: go/build: package could not be found locally
goinstall: url: go/build: package could not be found locally
goinstall: net: go/build: package could not be found locally
goinstall: sync: go/build: package could not be found locally
goinstall: runtime: go/build: package could not be found locally
goinstall: strings: go/build: package could not be found locally
goinstall: sort: go/build: package could not be found locally
goinstall: strconv: go/build: package could not be found locally
goinstall: bytes: go/build: package could not be found locally
goinstall: log: go/build: package could not be found locally
goinstall: encoding/binary: go/build: package could not be found locally

GOPATH is discussed in the cmd/go documentation:

The GOPATH environment variable lists places to look for Go code. On Unix, the value is a colon-separated string. On Windows, the value is a semicolon-separated string. On Plan 9, the value is a list.

GOPATH must be set to get, build and install packages outside the standard Go tree.

GOROOT is discussed in the installation instructions:

The Go binary distributions assume they will be installed in /usr/local/go (or c:\Go under Windows), but it is possible to install the Go tools to a different location. In this case you must set the GOROOT environment variable to point to the directory in which it was installed.

For example, if you installed Go to your home directory you should add the following commands to $HOME/.profile:

export GOROOT=$HOME/go
export PATH=$PATH:$GOROOT/bin

Note: GOROOT must be set only when installing to a custom location.

(updated version of Chris Bunch's answer.)

Here is a my simple setup:

directory for go related things: ~/programming/go
directory for go compiler/tools: ~/programming/go/go-1.4
directory for go software      : ~/programming/go/packages

GOROOT, GOPATH, PATH are set as following:

export GOROOT=/home/user/programming/go/go-1.4
export GOPATH=/home/user/programming/go/packages
export PATH=$PATH:$GOROOT/bin:$GOPATH/bin

So, in short:

GOROOT is for compiler/tools that comes from go installation.
GOPATH is for your own go projects / 3rd party libraries (downloaded with "go get").

First run go env.
If you see that the go isn't installed, you can install it via homebrew or via package and/or other ways.
If you are seeing output then your Go is installed.
It shows you all the envs that are set and are not.

If you see empty for GOROOT:

1. Run which go (On my computer : /usr/local/go/bin/go)
2. then export like this export GOROOT=/usr/local/go

If you see empty for GOPATH:

1. Create any directory anywhere on your computer for go projects in my case: ~/GO_PROJECTS
2. Then export GOPATH=~/GO_PROJECTS

GOPATH is discussed here:

The GOPATH Environment Variable

GOPATH may be set to a colon-separated list of paths inside which Go code, package objects, and executables may be found.

Set a GOPATH to use goinstall to build and install your own code and external libraries outside of the Go tree (and to avoid writing Makefiles).

And GOROOT is discussed here:

$GOROOT The root of the Go tree, often $HOME/go. This defaults to the parent of the directory where all.bash is run. If you choose not to set $GOROOT, you must run gomake instead of make or gmake when developing Go programs using the conventional makefiles.