Thistle is the common name for a number of species, some native, but an increasing number that are invasive, including many in the genus Cirsium, such as the bull thistle Cirsium vulgares. Once thistles flower, they rapidly go to seed and within a short time become highly invasive. They may even become the predominant species in fields and meadows, crowding out native and more valuable species. Therefore, despite their beauty, it is important to literally, nip them in the bud.
Put on heavy gloves to work with thistles. They have sharp spines all over--from the flower head to the rosette on the ground--and you will hurt yourself if you do not wear gloves.
Grasp the stem and gently pull the flower down where you can reach it (they can be quite tall), trying to avoid too much movement of the seed head if the bloom has matured and begun to disperse seeds. If the bloom is fresh or still a bud, and is not dropping seeds, skip the next step.
Hold the flower stalk in one hand and use the other hand to spray water over the fluffy seed heads. (They are lightweight, and will blow away in the breeze like dandelion seeds. Wetting weighs them down so they cannot easily disperse.)
Place a paper bag over the seed head and crimp it tightly around the stalk. (Tape to hold it shut at that point.)
Use a knife or machete to cut the stalk below the paper bag.
Cut the rest of the thistle to within a foot of the ground, then grasp the stalk and pull up the thistle root. (If it breaks you must dig it out with a shovel or trowel to kill the entire plant.)
Burn the paper bag with the thistle head inside (preferably, in a wood stove or other contained fire where no seeds can escape to reseed).