In order to create and clone dinosaur embryos, the dinosaur nucleus has to be created. A nucleus is a cell containing all of an organism's chromosomes (Source 1). After this, the nucleus has to be inserted into an unfertilised egg cell, known as an oocyte. The cell will multiply itself, forming a dinosaur embryo.
Since no non-avian dinosaurs survive today, no egg cells can be found. However, the egg cell of a heavily modified bird, such as a Chickenosaurus, could potentially be able to read the DNA of a small theropod, such as a Compsognathus or Sinosauropteryx. This is known as cross-species cloning (Source 2). Studies have suggested that birds are actually theropod dinosaurs (Source 3), so the chance of a chickenosaur egg reading the DNA of an actual non-avian dinosaur is relatively high.
However, the embryo will not develop into a dinosaur on it's own. The embryo has to be transported into an egg, or an artificial environment resembling an egg. Using the unfertilised eggs of modern birds is one option. However, the development and survival of an animal embryo depends on genetic and environmental influences (Source 4).
Another, better option would be to insert a fertilised dinosaur ovum into the uterus of a bird, possibly an emu or an ostrich (Source 5). An egg would then naturally form around it.
5. The Science of Jurassic Park And The Lost World Or, How To Build A Dinosaur, Rob DeSalle and David Lindley, 1997.