Treat digital exactly as you would film, there really is no difference. However depending on the camera used you may experience noise (film grain) at 400 ISO or higher. No one uses the term ASA anymore, but the values are the same as ISO.
Obviously you need a camera that will allow manual settings and or "bulb". Just go out and shoot photos as you did with film, but with one benefit, you can review the result immediately and adjust your setting if required.
You may find that on long exposures that your image may suffer from "hot" pixels. This would show as white specks on a dark/black background. If there are not too many "hot" pixels they can be removed very easily in an image editor.
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