Keep in mind when planting that Amethyst is thought of as hardy, so it can be safe to leave outdoors for the majority of winter (although if in doubt, using a row cover is often a good idea).
Growing Amethyst from seed
By our calculations, you should look at sowing Amethyst about 90 days before your last frost date.
Transplanting Amethyst
Ensure that temperatures are mild and all chance of frost has passed before planting out, as Amethyst is a hardy plant.