You shouldn't need to do anything if it's a standard Relate site. Have you tried creating a blog and search for that? 

Haven't yet. I'll try it later. Thanks.

I've just created a blog which I could use for testing the search functionality. And right on the Search button, I searched for test, freedom, countrymen and it just doesn't produce any results.

You can test it yourself if you must.

It doesn't work for some reason and I have no idea why because this is a default install.

I suggest you enable EPiServer error logging and check the log file. You will see the search service requests produced. I assume you have the search service installed in the same application in which case you should see requests to /IndexingService/IndexingService.svc (you might have to enable logging at the debug level)

You can try to browse to /IndexingService/IndexingService.svc where you should see a WCF service "endpoint not found" message. If that works, try to browse to the URL found in the log (/IndexingService/IndexingService.svc followed by some more or less long querystring). That can give more clues to what is wrong. It should return an atom document (xml).