Being auto-generated from the EB-Eye WSDL file, the documentation for the methods is the same as the one in their documentation pages.
First you have to create the client object:

private static EBISearchService ebiSearchService =
        new EBISearchService_Service().getEBISearchServiceHttpPort();

Then, if you only need a list of identifiers which satisfy your search term you can do it in one single step:

ArrayOfString resultsIds = ebiSearchService.getAllResultsIds(domain, query);

domain being one of the available indexed databases (see listDomains method). However this is discouraged as it can return a huge list. It is suggested to do it in two steps:

int numOfResults = ebiSearchService.getNumberOfResults(domain, query);
// and then page through numOfResults:
ArrayOfStrings resultsIds =
		ebiSearchService.getResultsIds(domain, query, start, size);

If you need more info from the search engine you will have to send more than one query, starting with getting the resultsIds (see above) and then:

ArrayOfArrayOfString entries =
		ebiSearchService.getEntries(domain, resultsIds, fields);

The fields will depend on the queried domain (there is a listFields method to know which fields are available) .

The EB-Eye offers more methods, including searching cross references from one domain to another one.