To install Cake PHP you first need to download the latest stable version from the CakePHP website at www.cakephp.org, once at the website click on Downloads > Release.
If you like living dangerously or are just curious you can also download a nightly snapshot of the CakePHP project from the nightly folder, however this is code still in development so there is no guarantees that it is stable.
For the stout of heart, you can also check out a fresh version of our trunk code using SVN. Check out a copy at svn://svn.cakephp.org.
Now that you've downloaded the most recent release, place that compressed package on your web server in the webroot. Now you need to unpack the CakePHP package. There are two ways to do this, using a development setup, which allows you to easily view many CakePHP applications under a single domain, or using the production setup, which allows for a single CakePHP application on the domain.