To search Hymnary.org, you can enter terms in the Search the entire Hymnary box in the upper right hand corner of the page, or for more specific or advanced queries, you can use the search sidebar on the left side of the page. Here are a few tricks that can help with searches:
Add a field: if you want to search by a field for which there is no box, you can add fields using the "Add a field..." drop box. For example, to search for a hymn containing the word "banner," click the "Add a field..." drop box and add the Full Text field.
Select result type: if you want to receive a list of a particular sort, such as hymnals, you can select it from the "Select result type" drop box. "Hymns" are published text/tune combinations.
The My Hymnals checkbox allows you to search only within hymnals that you own. You can add hymnals by logging in, clicking on your user name in the top right corner and then "My Hymnals". There you can select hymnals that you own and add them to the list. You can then check the "My Hymnals" checkbox to search within the hymnals in your collection.
More help is available on advanced searching.