The documentation can be written using the .auradoc file that is created every time you create a Lightning Component. The documentation for the Lightning Component is available at the https://<myDomain>.Lightning.force.com/componentReference/suite.app URL and any auradocs for custom components also appear at the same URL in your Salesforce instance. Note that <myDomain> is the domain name of your Salesforce instance.
As it currently has no documentation, you will see that the component docs for SearchApp look as follows:
Let's prettify it by adding the proper documentation. To start, let's add a description in the youtubesearch.auradoc file, as follows:
<aura:documentation>
<aura:description>
<p>An <code>SearchApp:youtubesearch</code> component...