Marigold belongs to the daisy family where a flower head is made up of many smaller florets. They are called composite flowers because individual flowers grow together to form what looks like a single flower. Marigold has several basic flower shapes. Single flowers found in French marigolds have broad petal-like ray florets around a central eye of tubular disc flowers. Semidouble or anemone-flowered marigolds have broad, flattened petals in overlapping rows around a smaller central disc. Double or carnation-type flowers have more rows of flattened petals. Crested flowers have tight clusters of disc florets surrounded by ray flowers. Double flowers occur in French and African marigolds, and are the result of hybridizing efforts begun in the late 1800s. The first double marigold was "Lemon Gold," released in 1905. To produce seeds, pollen from male anthers on one flower has to transfer to female stigmas on another flower.
Each floret has a female stigma that looks like a little "Y" and is sticky so pollen grains will adhere to it. Two male flower parts, the stamens, have pollen-producing anthers located to the sides of the stigma. All the florets are embedded in a fleshy base called the receptacle. When florets are pollinated, the ovary at the base of the floret develops and forms a slender spiky black seed. Each marigold flower head can produce many seeds. Honeybees, wild native bees and butterflies are the usual marigold flower visitors. As they crawl over the flowers, some of the pollen sticks to their bodies and mouthparts and gets deposited on stigmas of the next flower the insects visit.
To create new varieties of marigolds, planned crosses are made between already existing hybrids and species. Plant breeders remove stamens from one parent and rub them on receptive stigmas of another flower and then grow out the seeds. Some of the showy new varieties are the result of such orchestrated crosses, and the seeds for the hybrid variety are produced by making the same cross over and over and harvesting the F1 hybrid seeds. Often such hybrids won't be able to set seeds due to genetic incompatibility. Because hand pollination is involved in F1 seed production, hybrid seeds are more expensive.
If your garden marigolds come from open-pollinated seed and are isolated from pollination by other cultivars, it's likely that your seedlings will look like the parent plants. Flowers dry up after seeds form. When they are dry, cut them from the stem and put them upside-down in a paper bag. Separate the seeds from the dry flowers by breaking the flower heads apart with your fingers and separating the seeds from the chaff. Sort through the debris in the bottom of the bag to save seeds that have fallen out of the flower heads. Store the seeds in a paper envelope in a cool dry place until it's time to plant them.