Observations of transits of the hot giant exoplanet HD 189733b in the unresolved H i Lyman-α line show signs of hydrogen escaping the upper atmosphere of the planet. New resolved Lyman-α observations obtained with the STIS spectrograph onboard the Hubble Space Telescope in April 2010 and September 2011 confirmed that the planet is evaporating, and furthermore discovered significant temporal variations in the physical conditions of its evaporating atmosphere. Here we present a detailed analysis of the September 2011 observations of HD 189733b, when an atmospheric signature was detected. We present specific methods to find and characterize this absorption signature of escaping hydrogen in the Lyman-α line, and to calculate its false-positive probability, found to be 3.6%. Taking advantage of the spectral resolution and high sensitivity of the STIS spectrograph, we also present new results on temporal and spectro-temporal variability of this absorption feature. We also report the observation of HD 189733b in other lines (Si iii at 1206.5 Å, N v at 1240 Å). Variations in these lines could be explained either by early occultation by a bow-shock rich in highly ionized species, or by stellar variations.