The Standard or Traditional Classification of Dinosaurs uses the Linnean and evolutionary systematic approach.  This is confined now to older books.  There are two orders, the Saurischia and the Ornithischia, distinguished on pelvis structure (one being, as the name indicates, more lizard- or crocodile-like, the other more bird-like).  This basically goes as follows:

When various new types of dinosaurs were discovered - dromaeosaurs, segnosaurs, heterodontosaurs, etc - these were usually slotted in extra subdivisions; the dromaeosaurs for example were included with the coelurosaurs, and the heterodontosaurs with the ornithopods.  More recent books incorporate cladistic categories - e.g. Cerapoda, Maniraptora, Marginocephalia - but this introduces so many extra levels that the Linnean system breaks down.. Moreover, even the most recent dino books still retain the Saurischia-Ornithischia dichotomy (Herrerasaurs for example are usually included under the Saurischia).

A more controversial classification of the Dinosauria is presented by Gregory S. Paul in his Predatory Dinosaurs of the World (1988), to my mind still the best book on dinosaurs ever written (albeit looking rather dated and with some rather dubious metabolic asusmptions).  GSP suggests the following arrangement (based in part on Robert T. Bakker):

These inflated taxonomic rankings appear to be an attempt to reconcile the Linnean and Cladistic systems; generally such attempts don't work.

Stanley Friesen's  Preferred Classification of the Dinosaurs is based on the conventional two order arrangement differs somewhat by incorporated new taxa and discoveries, but avoids cladistic approach

Full Linnean Classification combines the cladistic and the Linnean by adding division, subdivision etc

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