We compare Hα, ultraviolet (UV) and infrared (IR) indicators of star formation rate (SFR) for a well-defined sample of z = 0.84 emission-line galaxies from the High-. z Emission Line Survey (HiZELS). Using emission-line, optical, IR, radio and X-ray diagnostics, we estimate that 5-11 per cent of Hα emitters at this redshift are active galactic nuclei. We detect 35 per cent of the Hα emitters individually at 24 μm, and stack the locations of star-forming emitters on deep 24-μm Spitzer Space Telescope images in order to calculate the typical SFRs of our Hα-emitting galaxies. These are compared to the observed Hα line fluxes in order to estimate the extinction at z = 0.84, and we find a significant increase in dust extinction for galaxies with higher SFRs. We demonstrate that the relationship between SFR and extinction found in the local Universe is also suitable for our high-redshift galaxies, and attribute the overall increase in the typical dust extinction for z = 0.84 galaxies to an increase in the average SFR, rather than to a change in dust properties at higher redshift. We calculate the UV extinction, and find a similar dependence on SFR to the Hα results, but no evidence for a 2175 Å UV bump in the dust attenuation law for high-redshift star-forming galaxies. By comparing Hα and UV indicators, we calculate the conversion between the dust attenuation of nebular and stellar radiation, γ, and show that γ = 0.50 ± 0.14. The extinction/SFR relationship is shown to be applicable to galaxies with a range of morphologies and bulge-to-disc ratios, to both merging and non-merging galaxies, and to galaxies within high- and low-density environments, implying that it is a fundamental property of star-forming regions. In order to allow future studies to easily correct for a SFR-dependent amount of dust extinction, we present an equation to predict the extinction of a galaxy, based solely on its observed Hα luminosity, and use this to recalculate the Hα luminosity function and SFR density at z = 0.84.