I have grown tarragon for quite a long while; however, I always thought mine was the desirable French tarragon (Artemisia dracunculus). However, that species is said not to flower, whereas mine has pretty sprays of petite, bright golden blooms in late summer and autumn. Mine has tasty leaves, so can't be the Russian form (Artemisia dracunculoides), so I have concluded it is the Mexican - or winter - tarragon, Tagetes lucida. The flowers are like miniature versions of the mountain marigold, Tagetes lemmonii.
I have always grown my tarragon in a pot, where it does quite well. However, it does need regular division to stay healthy in a container, so another option is to plant it in a sunny place in the garden. It grows about 60 cm tall, and dies down in winter, to re-emerge in spring. The long, slender leaves taste of aniseed and are useful in cooked dishes and salads. Propagation is by division or cuttings taken in late spring.