When you click on the lookup icon, let's say to a contact from an opportunity, the layout has certain fields. In this case, it's only showing Name and Account Name which isn't very helpful. Let's change the layout to show more helpful fields.

In setup, navigate to the Search Layouts link for the object that is where the records are. Even though you might have clicked the lookup icon on an opportunity, the layout you're changing is for the records that are being displayed. In this case, it's Contacts.

Note: If the object is a custom object, you can find it under the Create > Objects > Name of Object menu. The Search Layouts are in a section lower down on the custom object page.

Click Edit to the left of Lookup Dialogs.

Modify the page to show the fields you want and remove any that you don't. When satisfied, click Save.

Now lookup dialogs will have the fields you selected.