The Neoclassic period, like all other periods, was a reaction to the period which preceded it, the Renaissance period. The Neoclassists focused upon the importance of order and restraint. No longer were texts filled with overzealous ramblings; instead, the texts became simplified by the authors using only conventional literary devices- and only when absolutely necessary.
The texts focused upon the ideals as stated by the classics- this typically involved the order and peace (which came from order) embraced by the Roman Empire. Neoclassists believed that mankind was constant in their behavior. Therefore, the ability to succeed or fail has already been proven in the past. They believed that one should not try to set goals which existed far beyond rational reasoning; instead, goals should be simplistic so as to insure success.
John Dryden's poems were created using classic forms (showing usage of classic ideals) and focused upon the facts.
Alexander Pope's poems, mirroring Dryden, were typically written in heroic couplets. But, instead of adhering to the modes of the classic poets, Pope (in An Essay on Criticism) wished to define himself as a true poet. In the text, Pope examines the techniques used by the classic poets so as to define himself as a poet. Pope achieves this by giving credit to the classic poets regarding their authority on the matter and then shows the importance of adhering to specific attributes.
Oliver Goldsmith would not be considered a Neoclassist given he did not adhere to any specific school or ideal. One could loosely justify "An Elegy on the Death of a Mad Dog" as an example of neoclassic poetry solely based upon the fact that the poem supports sensibility and decency.