It is probably best to use the semi-automatic installation procedure described earlier. See Installation of the REDUCE IDE. But if you want to install by hand, or understand the details of the installation process, then read on ...
REDUCE run mode requires the library reduce-mode both when it is compiled and when it is loaded. It tries quite hard to locate this library, but normally it should be in the same directory as reduce-run.
Byte-compile the file reduce-run.el, put the result somewhere in
load-path, and put the following in your .emacs file:
(autoload 'run-reduce "reduce-run" "Run a REDUCE process" t)
If you would like to have automatic full access to the features of REDUCE run mode from REDUCE edit mode then also put the following in your .emacs file:
(add-hook 'reduce-mode-load-hook 'require-reduce-run)