I heard "zay sefer" as well rather than "zay hasefer" and wrote the same thing you did (it was marked right - I got away with a "typo"). Normally I have no problem hearing the definite article in these audio exercises, but it is extremely subtle this time. This is the sort of situation where the "turtle" option (i.e. ability to slow the audio down) would come in handy.
That would be simply "זה ספר". Just drop the definite article (the letter hey) from the start of the word for book. Hebrew doesn't use indefinite articles. It also doesn't really have a verb for "to be" (at least not in the present tense - not sure about other tenses). So it's literally "this book", but of course for it to make sense in English, we would say "this is a book".
Don't know if you've tried Russian, but that has a very similar sort of construction. In that language you would say (and please forgive the lack of Cyrillic letters here) "eto kniga", with "eto" meaning "this" or "this is" and "kniga" (or "knigo", however you spell it) meaning "book" or "a book". Other Slavic languages do something similar.
So Hebrew is not unique in this type of construction, but anyway, that's all you have to do to say "This is a book".
Incidentally, to actually say "this book" as opposed to "this is a book", you need to say "הזה הספר" - so add the "hey" definite article to both words.