For built in objects in Salesforce (eg Contacts, Accounts, Campaigns, etc), you can add fields to the Lookup Dialog by doing the following:
  1. Go to Setup -> Customize -> the Lookup object (Contact, Account, etc) -> Search Layouts.
  2. Click Edit next to Lookup Dialogs.
  3. Move the fields that you want in the Available Fields column to the Selected Fields. 
  4. Click Save. 

For Custom Objects (eg Tributes, Recurring Gifts, etc) edit the fields of the Lookup Dialog by doing the following: 
  1. Go to Setup -> Create -> Objects -> the Lookup object (Tribute, Recurring Gift, etc). 
  2. Under Search Layouts, click Edit next to Lookup Dialogs. 
  3. Move the fields that you want in the Available Fields column to the Selected Fields. 
  4. Click Save.