On an advanced or saved search page, on the Criteria or Results subtab, select the previously defined custom field and set criteria as for any other custom field. Click OK. Click Submit to view your search results.
If the searches are returning static values for a custom formula field instead of recalculating when new data is entered into the system, the field may have been defined to store the value for the calculation at the time of record creation. This is controlled by the Store Value box on the custom field definition. Check if the value should be dynamically calculated at the time of every search.
Results for Formula (Text) fields will only be displayed as plain text to improve the security of saved searches. To prevent issues with your searches, you should replace your Formula (Text) fields with the new Formula (HTML) field and check the Disable HTML in Search Formula (Text) box at Setup > Company > General Preferences.