How to install a Joomla! component is beyond the normal range of documentation that component authors provide, 30 seconds after you figure it out, you'll agree with me.
If the documentation is that complete, it will be huge and scare off the people it is intended to help. Your difficulty in finding the component for download is a timing issue. The 1.5 version is under heavy development and Geraint has been posting SVN builds in this
forum thread. This is not the normal distribution method. I've been downloading the SVN code and installing from there for about a year as I followed the progress of version 1.5, now that's the hard way.
To your question about installation: download the component (required) and the modules and plugin (optional) from the thread that I referenced above. In the administrative (back end) screen of your Joomla! installation, select Extensions and Install/Uninstall from the top menu. The "normal" way is to use the top section of the install screen, "Upload Package File." Use the browse button to find the component file that you downloaded to your local computer and select it. Next, press the "Upload File & Install" button. You should get a success message when the install is complete. Repeat the same process for the modules and plugin.
You will need to create a new menu item in Joomla! pointing to your JEvents component. You can publish the modules in any module position that you want in your site template from Extensions, Module Manager. You need to publish the search plugin from Extensions, Plugin Manager. There is quite a bit to the after installation configuration of the component, but the online help will guide you through most of that. If you have further questions about setting up JEvents, post your question on the forum. Geraint is a support demon, it is tough for a community member to find a question he hasn't already answered.
Good luck with it.