Making night time Time Lapses is a bit more complicated.
Focus - super sharp focus isn't necessarily what you are after. Having your stars ever so slightly out of focus will make them stand out more in the final video.
Swing your camera over to a bright star, a planet or the Moon to get focus. You will only frustrate yourself if you try to focus on fainter stars.
Exposure time - Point and shoot cameras generally only go up to 15 second exposures. To make the most of that time, set your ISO as high as you can (keeping in mind that the higher the ISO the more noise you will have in the pictures ) and your F stop as low as it will go.
DSLR's without remote timers or shutter releases are the same. You have only 30 seconds to capture as much light as you can so ISO 1600 - 3200 and a low F stop are necessary.
Hooking up a Digital Timer Remote to your DSLR is ideal for this sort of work. Set your camera to "Bulb" then set your timer exposure to around 1 minute (do a test shot to make sure there isn't too much star trailing ) and again, ISO 1600 - 3200 and a low F stop.
Interval - For night time work go with an interval of 1 minute between shots, it will give a smoother final video than say a 4 minute inteval.
Use your Digital Timer Remote or do this manually as explained previously.
If you aren't using a Timer Remote, don't forget to set your cameras built in timer to 2 seconds to prevent camera shake.
It's not unusual for dew to start to form on the lens during the course of the night. Be mindful and check from time to time. A short blow of warm air from a hair dryer during the interval time is all that is needed.
You can process your night time shots the same way as you did the day time ones.
I hope this was comprehensible. I tried to keep it as basic as possible. If you have any question please ask.