The University of Sydney Library is open to the public. As long as the item you are looking for is not in Storage or Rare books, then you can just show up and have a read.
If the book is in Storage, then only Library members can request the item. If the book in question is in Rare books then you would need to notify them in advance so that they prepare the item for viewing.
Please check our catalogue to see where the items you want then check the library's opening hours to make sure it is open at the time you want to come.