How to add custom fields to a page
Drupal allows content to go onto your site, such as a Page or Book through a content type. If you want to show a Page or Book and embed a field or form on that page that is backed by a database -- typically you have to use another module for that which allows you to embed Forms onto existing Page (Node) content.

To do this usually you can use 1 of the following modules:

Webform


  Webform is the module for making forms and surveys in Drupal. After a
  submission, users may be sent an e-mail "receipt" as well as sending a
  notification to administrators. Results can be exported into Excel or
  other spreadsheet applications. Webform also provides some basic
  statistical review and has an extensive API for expanding its
  features.
  
  Some good examples could be contests, personalized contact forms, or
  petitions. Each of these could have a customized form for end-users to
  fill out. If you need to build a lot of customized, one-off forms,
  Webform is a more suitable solution than creating content types and
  using CCK or Field module.


or

EntityForms


  The Entityform module enables you to create front-end forms (fieldable
  entities), which contain fields that you define! These forms use the
  standard Drupal fields. This means that out of the box, you can use
  any standard Drupal node field!


These modules allow you to embed any form you define through their admin interface into existing page content.

A key difference is in these forms is that Webforms stores its own data in a custom backend difficult to make into drupal (page) content on your website. While EntityForm since it uses Drupal Fields -- it's submitted content may easily be turned into Drupal site content (but need not be).