Deadheading is the single most important garden job to keep flowers blooming for as long as possible. And it's really quite easy. Snip off all of a plant's spent flower stalks just above the next set of leaves. Monty Don recommends you do it every day, but for most of us, a couple times a week should be plenty.
This is what the stem should look like after deadheading: A short stub just above a set of leaves.
To understand why deadheading works, you have to think like a plant. From the plant's perspective, the point of flowering is to attract insects that will pollinate the flowers to create seeds and reproduce. When a plant makes flowers, it's intending to make seeds. Once the flower is pollinated and begins to fade, the plant will put all its energy into those developing seeds, and stop producing new flowers.
If you cut off the faded flowers, the plant continues to put its energy into flower production, hoping to get pollinated and create seeds. The less time a plant spends with pollinated flowers, (i.e. the more frequently you deadhead) the more flowers you'll get.
Calendula goes very quickly from flower to seed head. If these aren't snipped off, the plant will focus its energy on the seeds and stop producing flowers.
I snip the spent flowers at the base of the stem.
Just a little stub of stem is left behind
This same principle applies to harvesting vegetables too. For many of our homegrown crops (zucchini, tomatoes, green beans), we eat the fruit and seeds. Because fruit follows flowers, we definitely don't want to deadhead the flowers!
(Anecdotal asides: I met someone who picked all the flowers off her tomato plants because she thought they were getting in the way of growing tomatoes. You can imagine she was puzzled by the lack of tomatoes. Another time, I helped a colleague of mine plant tomatoes in his yard. One day, he told me he noticed that the tomatoes seemed to form right where the flowers had been, and wasn't that fascinating? I was A, surprised that he could get to 55 years old without knowing that and B, impressed that he figured it out, just by keeping an eye on his first ever tomato plants. Goes to show that, as I often say, much of gardening is in observation.)
Anyway, we eat those fruits and seeds at an immature stage. The plant might like to continue putting energy into developing seeds, but because we pick and eat them, the plant produces more. So for all the summer fruiting veggies, stay on top of harvesting them to keep the plant producing over a longer season.