A fast prime gives you a few more stops of light than your kit lens, usualy 2-4 stops, meaning 4-16 times the light is hitting the sensor.
A tripod allows you to expose longer, so instead of 1/20 second handheld, you can do 30 second exposures wich give you 600 times the light on top of that.
Image stabilisation may also help you to expose longer.
My typical handheld night setup (APS-C) is>35 mm f/2 >manual mode>aperture f/2>1/20 second>ISO automatic
That way I have the least noise I can reasonably archive without fear of shake.
My alternative setup is:>18-55 mm f/3.5-5.6 IS>manual mode>18 mm f/3.5 IS on>1/5 second>ISO automatic
And on the tripod I just go up in exposure time as high as reasonably possible, often 30 seconds or a few minutes with the lens stopped down a little and rather low ISO.
Oh, and your AF may not work if it's too dark, so get good at manual focusing.