We report on the setup and initial discoveries of the Northern High Time Resolution Universe survey for pulsars and fast transients, the first major pulsar survey conducted with the 100-m Effelsberg radio telescope and the first in 20 years to observe the whole northern sky at high radio frequencies. Using a newly developed 7-beam receiver system combined with a state-of-the-art polyphase filterbank, we record an effective bandwidth of 240 MHz in 410 channels centred on 1.36 GHz with a time resolution of 54 $mu$s. Such fine time and frequency resolution increases our sensitivity to millisecond pulsars and fast transients, especially deep inside the Galaxy, where previous surveys have been limited due to intra-channel dispersive smearing. To optimise observing time, the survey is split into three integration regimes dependent on Galactic latitude, with 1500-s, 180-s and 90-s integrations for latitude ranges $|b|<3.5^{circ}$, $|b|<15^{circ}$ and $|b|>15^{circ}$, respectively. The survey has so far resulted in the discovery of 15 radio pulsars, including a pulsar with a characteristic age of $sim18$ kyr, {PSR J2004+3429}, and a highly eccentric, binary millisecond pulsar, {PSR J1946+3417}. All newly discovered pulsars are timed using the 76-m Lovell radio telescope at the Jodrell Bank Observatory and the Effelsberg radio telescope. We present timing solutions for all newly discovered pulsars and discuss potential supernova remnant associations for {PSR J2004+3429}.