Hi Vivi, and welcome to RPF.
Are you using film or digital capture?
I suspect that the blurring is mostly due to the slow shutter speed that the low light conditions require and the only real solution there is to provide a more stable platform for the camera. This could be a tripod, but even holding the camera against a static object such as a lamp-post, the roof of a car or similar can make a huge difference.
The graininess can be exploited as a ‘feature’ of a low-light image and can add significantly to its aesthetic. However, there are ways to reduce it by choosing either a film with greater sensitivity (high ISO rating), using higher ISO setting on a digital camera or a camera with a larger sensor.
Taking a meter reading at night is often prone to error, either because of the poorer sensitivity / accuracy of many meters in low light and also because of the dominance that even small point sources can have on the reading you obtain. This will result in dark images. Avoiding such highlights and using a more-point source way of metering can help, especially if you meter off of areas that are providing ‘moderate’ levels of refection of the light available (eg road surfaces).
Does that help?