Break it up into pieces.

• You can write one module that controls access to the database. This should have add, delete, update, and list methods.
• The quotes themselves could be objects with methods to provide the quote itself, its author, etc.
• The web interface could be modularized depending on how you intend to implement it and what webserver and application framework you're working with.

Doing the database as a module allows you to easily substitute another implementation that saves to text files, a different database, db files, or whatever.

Doing the quotes as an object allows you to write a command line utility that accesses the quotes.