We know what a nova is, but how? I work with astrophysicists and require some basic knowledge of many astronomical sources, however research priorities often demand that most of human knowledge on a subject be taken for granted.

I am currently researching galactic novae, and I find it relevant to summarize their history briefly when presenting my research to certain audiences. Unfortunately, I am unable to find any source material which describes how we know one key aspect of the events: that they are an accreting white dwarf in a stellar binary. This fact appears to be so well founded that no scientific paper feels obligated to cite it when stated, but basic resources like astronomical encyclopedia also make no reference that I've seen.

How do we know that novae are binary systems?

E.g., have follow-up observations clearly identified the white dwarf and its companion? Or do other astronomical measurements strongly confirm this binary hypothesis (and make it all but obviously true)? I apologize if it's as simple as "someone looked through a telescope, and it was pretty obvious" -- in my experience no revelation in astrophysics is nearly so simple, but certainly this could be the case.
Following a reference to Darley et al., ApJ 746, 61 (2012) from your Wikipedia link gives a (very technical) discussion of nova progenitors, including distinctions between nova systems where the secondary stars are main sequence or supergiant stars, and distinctions among white dwarfs with different chemistries.
The first sentence of that paper is 


  A classical nova (CN) outburst occurs in an interacting
  binary system comprising a white dwarf (WD, the primary) and
  typically a late-type main-sequence (MS) star (the secondary)
  that fills its Roche lobe (Crawford &amp; Kraft, 1956).


That suggests the 1956 paper is the original proposal for the Roche overflow model of the classical nova.
Like many original-idea papers, it's a pretty clear read.
But for your question, Crawford and Kraft seem to hedge about whether the "blue star" in their particular pair needs to be a white dwarf:


  [T]he
  observed
  luminosity
  of
  the
  blue
  star
  is
  essentially
  due
  to
  the
  energy
  released
  by
  the
  accreted
  material.
  This
  view
  is
  strengthened
  also
  by
  the
  fact
  that
  the
  blue
  star
  occupies
  a
  peculiar
  position
  in
  the
  H-R
  diagram.
  It
  lies
  10.5
  vis.
  mag.
  below
  the
  main
  sequence
  but
  about
  4
  mag.
  above
  the
  most
  luminous
  white
  dwarfs,
  whose
  effective
  temperature
  it
  exceeds
  by
  about
  8000°
  K.
  Unless
  the
  blue
  star
  is
  essentially
  degenerate,
  it
  can
  readily
  be
  shown
  that
  the
  small
  radius
  implies
  such
  a
  high
  internal
  temperature
  that
  electron
  scattering
  is
  the
  principal
  source
  of
  opacity.
  A
  simple
  calculation
  based
  on
  the
  standard
  model
  then
  yields
  a
  luminosity
  8
  mag.
  brighter
  than
  is
  observed.


In other words, Crawford and Kraft don't come out and say "definitely a WD," but if it's a non-degenerate star, it's a very strange one.
More modern observations of novae are compared to detailed models of the dynamics of the surface dynamics, models which have been debated vigorously for decades; the current generation of comparisons to data are sensitive to details like the amount of helium accumulating on the white dwarf's surface during the nova event. It seems unlikely that such details could even come close if the underlying assumptions about the basic physics of the erupting star were wrong.

Note that a classical nova system can be thought of as a type of contact binary star.
For any reasonable estimate of the size of the giant star, a distance of 10 AU between the two members of the pair seems like an overlarge estimate.
Ten astronomical units of separation viewed from a distance of 50 parsecs is already a gap of 0.1 seconds of arc. I wouldn't expect to see visible-light photographs showing both the giant star and the white dwarf, but rather that all of the information about the binary systems comes from spectroscopy.