They are actually viewed as an annual so you need to grow from seed each year. You can try saving the seed and sowing next year but you will not necessarily get the same flowers as the parent plant and, if this is an F1 hybrid, the seeds will be sterile.

Thanks Moon growe

Actually, MG, F1 Zinnias are not sterile, but they will show even more variation in their seedlings than an open pollinated variety, and the seedling's flowers are more likely to be smaller and more open than their parents'.

I stand corrected :-)

I am SUCH a schoolmaster! : )