Once you have all of the necessary components and place them into the Embryonics Machine, you will get a syringe filled with the Embryo of the particular species in question.
If the species is a plant, you need to first combine a Petri Dish containing Agar with a source of plant cells. Obtain a syringe with plant cells by right-clicking on any plant with an empty syringe. Combine the two in a crafting grid to get a Petri Dish with Plant Cells. Place the Petri Dish with Plant Cells, an empty syringe, and the physical DNA sample of a plant, in the Embryonics Machine to get Plant Callus.
Right-click on Farmland with the Plant Callus to get your plant!
If the species is an egg-laying animal however, you'll need an Embryo Calcification Machine.