First go to Control/BookshelfScreen (on the iPhone look under the More tab) and toggle on the Search bar switch.

After that:

1. Select the iPad bookshelf (or any of those under Cataloguer)
2. In the middle of the screen, swipe downwards with one finger
3. A search box appears
4. Type in the phrase you wish to search for
5. The phrase is searched for (insensitively) in the Title, Authors, and Subjects fields

Note that the search is for an exact string, not the individual words in the string.

Remember that you can also view books categorized by their metadata in the Cataloguer screen.

For more detailed searching, read the 'How to limit book searches to author, title, etc.' FAQ.