Context. V407 Cyg was, before 2010 Mar., known only as a D-type symbiotic binary system in which the Mira variable has a pulsation period of approximately 750 days, one of the longest known. On 2010 Mar. 10, it was discovered in outburst, eventually reaching V < 8. This is the first recorded nova event for this system, but it closely resembles the spectroscopic development of RS Oph, the prototypical symbiotic-like recurrent nova. It was also detected by Fermi above 100 MeV and displayed strong, likely nonthermal centimeter wavelength radio emission. Aims. Unlike classical novae occurring in compact cataclysmic binary systems, for which the ejecta undergo free ballistic expansion, this explosion occurred within the dense, complex wind of a Mira variable companion. This paper concentrates on the development of the shock and its passage through the Mira wind. We also present some constraints on the binary system properties. Methods. Using medium and high resolution ground-based optical spectra, visual and Swift UV photometry, and Swift X-ray spectrophotometry, we describe the behavior of the high-velocity profile evolution for this nova during its first three months. Results. Using the diffuse interstellar bands visible in the high-resolution optical spectra, we obtain an extinction E(B − V) ≈ 0.45 ± 0.05. The spectral type of the red giant during this period, when the star was at R minimum, was no earlier than M7 III. The peak of the X-ray emission occurred at about day 40 with a broad maximum and decline after day 50. The main changes in the optical spectrum began at around that time. The He II 4686 Å line first appeared between days 7 and 14 and initially displayed a broad, symmetric profile that is characteristic of all species before day 60. The profile development thereafter depended on ionization state. Low-excitation lines remained comparatively narrow, with v rad,max of order 200-400 km s −1 . They were systematically more symmetric than lines such as [Ca V], [Fe VII], [Fe X], and He II, all of which showed a sequence of profile changes going from symmetric to a blue wing similar to that of the low ionization species but with a red wing extended to as high as 600 km s −1 . The [O I] 6300, 6364 doublet showed a narrow wind-emission component near the rest velocity of the system and a broad component, 200-300 km s −1 , whose relative intensity increased in time. Forbidden lines of N II and O III had two separate contributors to the profiles, a broad line that increased in strength and velocity width, exceeding 200 km s −1 , and narrow components from a surrounding ionized region at higher velocity than the Mira wind. The Na I D doublet developed a broad component with similar velocity width to the other low-ionization species. The O VI Raman features observed in recent outbursts of RS Oph were not detected. We interpret these variations as aspherical expansion of the ejecta within the Mira wind. The blue side is from the shock penetrating into the wind while the red wing is from the low-density peri...