What techniques does Baz Luhrmann used to transform Romeo and Juliet into a contemporary context?

I would say that one particular technique that Luhrmann
uses is a modern soundtrack.  At least by the standards of the late 1990s, the musical
soundtrack that accompanies the film is quite modern and contemporary.  Musical
performances by Garbage, Everclear, and Radiohead brings out the "Grunge" feel of the
time period, contemporarizing his film and forging another link between the viewer and
the Shakespearean text.  The style of filming is radically different than a traditional
cinematic depiction.  Luhrmann uses fast paced filming with quick cuts and a distinct
"MTV" style to bring out another link between the viewer and the text.  The use of
modern sportscars, settings, and guns also helps to make the feel of the work
contemporary, feeding into a set design technique that allows a modern feel to emerge. 
Verona Beach as the setting of Verona works well in bringing out the contemporary feel. 
These help to bring out a contemporary take on the Shakespearean
work.