Instead of throwing away beautiful flowers that people have given me, I've started making a habit of drying them so that I can enjoy them for years. There are three basic methods to preserving flowers. One way is to press them in a book. I do that a lot when I find little wildflowers on road trips or just when I explore around our property (and our neighbor's). It's good to use wax paper so that you don't damage the book; plus it squishes all the little buggies that might be hiding in the flowers.
Another method I know of involves covering the flowers with wax to preserve them, but I have never done that so not much more can be said from me.
The third method (Golly I sound like I'm writing a research paper) is to dry them by hanging them upside down. This way all the moisture runs out of the flowers so that no mold can grow on them (flower mold is extremely gross, take my word for it). It leaves most of the color in the flowers, although as you could guess they are extremely dry and sometimes crumble when you accidentally handle them too hard. But I have found it is a virtually stress free method.
I have a little nail in the ceiling beam in my loft from which I just tie a string to the flowers. They hang there for about two weeks, I would say (quite honestly I just forget about them and whenever they come to mind I check on them). Once these flowers from yesterday's homecoming are dry, I'll take them down and add them to my vase of pressed flowers. Soon I'll have to get a bigger vase! Then whenever I look at them I can remember all the beautiful memories that went along with them.