I have a very old computer which is running Lubuntu 12.04. I don't think it can be upgraded to 14.04 as it is non-pae. The Lubuntu software center does not provide any Adobe Flash Player installation. I have downloaded the flash-plugin 188.8.131.525 release.i386.rpm. Please excuse my ignorance; but how do I install it from there?
You cannot install rpm. This is package for another distribution (Fedora, RHEL and its derivates). You can try this HOWTO on webupd8 or you can try installing flash player from repository - open terminal and run this command:
sudo apt-get update && sudo apt-get install flashplugin-installer
It will update your package database and installs package named
flashplugin-installer if it is present in your repositories.
If you want to download from the site choose APT for Ubuntu version. It is the supported format for your system.
Also note that Lubuntu uses the same repositories as Ubuntu, so you can install from official Ubuntu repositories, as well. Just make sure you have enabled Canonical partners repository in your package manager (Software Center or Synaptic).
I have downloaded the flash-plugin 184.108.40.2065 release.i386.rpm. Please excuse my ignorance; but how do I install it from there?
You do not; well it is possible with the "alien" tool to convert it into a .DEB file but that file is intended for Redhat and/or CentOS.
You need to find either a file ending on .DEB or .tar.gz. From the package list I believe you need this (edit: byran has a good option too).
I don't think it can be upgraded to 14.04 as it is non-pae
You probably can; you need to download the
ubuntu-14.04-desktop-i386.iso version from the download site. Well if it meets all the normal requirements that is.