After every shower, pull the curtain closed, making sure it lies flat. This will provide air exposure and the curtain will dry faster. If the curtain is pulled to one side and left this way, it becomes a breeding ground for mold. This can be a health risk to your family.
If you use a curtain liner, you can toss this in the wash once a month (or more often, depending on how many showers are taken daily). A frosted liner with magnets in the corners will work just fine for up to 3 months and are rather inexpensive. (under $4). You can attach a beautiful fabric curtain that hangs outside of the tub so no one will see the liner.