These can be any (finished) size from A6 to A4, using a variety of materials and paper weights depending on your budget. Thicker card covers and laminated covers available.
There is often some confusion when specifying booklets. Please indicate the number of pages (sides) - which must be in multiples of 4 - and whether this includes the cover. The stated size should be the finished size of the book after folding. For example if you take 2 sheets of A4 paper and fold them in half this would make an A5 8pp (page) booklet.