This answer is meant for users of Unix and Unix-like systems. Users of other operating systems should see the series of questions beginning with Emacs for MS-DOS, which describe where to get non-Unix source and binaries, and how to install Emacs on those systems.
Most GNU/Linux distributions provide pre-built Emacs packages. If Emacs is not installed already, you can install it by running (as root) a command such as ‘yum install emacs’ (Red Hat and derivatives) or ‘apt-get install emacs’ (Debian and derivatives).
If you want to compile Emacs yourself, read the file INSTALL in the source distribution. In brief:
ftp://ftp.gnu.org/pub/gnu/emacs/emacs-VERSION.tar.gz
(Replace ‘VERSION’ with the relevant version number, e.g. ‘23.1’.)
gzip and tar programs, which are
standard utilities. If your system does not have them, these
can also be downloaded from ftp.gnu.org.
GNU tar can uncompress and extract in a
single-step:
tar -zxvf emacs-VERSION.tar.gz
cd emacs-VERSION
./configure # configure Emacs for your particular system
make # use Makefile to build components, then Emacs
If the make completes successfully, the odds
are fairly good that the build has gone well. (See Problems
building Emacs, if you weren't successful.)
make install
Note that ‘make install’ will overwrite /usr/local/bin/emacs and any Emacs Info files that might be in /usr/local/share/info/.