Flowers form to make seeds for the survival of the species.
Flowers have a life cycle: new, vibrant, fading, dried, seed head.
What you did is correct: it is called deadheading.
It stimulates new flowers to come out in order to create seeds for survival of the species.
On zinnias, just cut the old flower stem down to where you see new buds or shoots (branches)developing on the stem. Your new flowers will appear there. Keep doing this all season to make bushier and more heavily flowered plants.
Everything is normal, your instincts are correct. All the language you are unfamiliar with is superfluous and you will learn by doing: then you will understand the language as you see the results of your actions. No worries!

Well, it looks as though deep_roots covered the whole question :)

The only thing I can add is: don't hesitate to ask whenever you come across a new (strange, peculiar, and/or incomprehensible) word or phrase. first: If it's new to you, then it's new to someone else and it really should be explained; and second: in gardening, there is often more than one way to do or say something, and this is a great forum for getting answers from many different people.

Thank You both for your prompt responses... I am very excited to watch how these grow! :-)

My zinnias were GLORIOUS all summer and fall. Of course, they all turned brown overnight with the first freeze. Since I want to do this again in the spring, should I:
A) cut the plants down leaving the roots? (I know they're an annual, but is there any possibility of their staging a comeback next year?)
B) crush the flowers and allow them to naturally scatter the seeds in the same spot? Maybe even plant the flowerheads to sew the seeds?
C) just be thankful they bloomed for so long, toss them into the compost bin, and buy new zinnia plants next year?

What should I do? Suggestions welcome. Thanks in advance.

Hi & welcome to Gardenweb!

"I know they're an annual, but is there any possibility of their staging a comeback next year?"

Many plants sold "as annuals" are actually perennials that can't live permanently where they are being sold. A true annual completes its' life cycle after blooming.

Zinnias are true annuals. Easily grown from seeds, whether those you saved or by buying them in the spring. If the seeds weren't already ripe, saving frozen flowers will not likely yield viable seeds. Most seeds can handle a freeze after they are ripe, but I don't know if that holds true for Zinnia seeds.

I plant my zinnias and marigolds from seeds every year. I did save the seeds from the dead flowers and scattered them in the garden in the spring. Now i start them in small pots at the beginning of spring and have a good crop all summer.