Installation
Installing the component is nothing different from standard Joomla component which is explained here:
http://docs.joomla.org/Installing_an_extension
Setup
The setup of component involves the following steps:
Author Categories
A quote is said by an author, be it yourself or someone else. So you can add Author Profile during quote creation process which includes entering Author details and selecting a category for Author.
You can create author categories from Components->Community Quotes->Author Categories page.
Quotes Categories
Just like authors, each quote is assigned to a category. For example, Inspiration Quotes etc.
You can create Quote Categories from Components->Community Quotes->Categories page.
Options
The basic configuration settings and permission settings are accessible from Options button on toolbar. Click on the Options button on toolbar and you will be shown the page with all configuration options/permission settings available. Make sure to configure permission settings as per your needs. You can allow front-end users as well to create the quotes/authors.
Menu Items
Once the configuration is complete, you need a menu item to access the component on front-end. Create the menu item for Community Quotes just like any other component and you are good to go. Here is the basic steps explained about menu creation process:
http://docs.joomla.org/Adding_a_new_menu_item
Now the component is ready to accept your and your users input.