The New Entity Search form is opened from the Add button of the entity search form:

The following fields are available:
Name: Enter the name of the search. This must be unique and not clash with existing searches.
Entity: Choose from a list of entities. This list is as follows:

Based Upon: This is the queries which exist for the chosen entity above. Some queries contain fewer fields than others. In general, queries returning fewer fields are faster than those returning many fields and this may be an issue for certain searches.
Description: This is the description of the search. If this is left blank, the name of the search is copied to this field for convenience.