You need to dry the rose as soon as possible, before it wilts.
If the air in your home is dry and warm, hang the rose upside down over a heater or in front of an AC outlet by a piece of yarn you tie to the stem. Do not hang it in direct sunlight or it'll lose its color. Spraying the flower with ordinary hair spray before drying it helps keep all the petals in place. The petals will shrivel up a little bit, but the overall shape of the flower will be well preserved and the flower won't bee too delicate or brittle.
If the air is cool or humid, dry the rose by surrounding it in a desiccant. There are different desiccants that work for this purpose, like:
- Silica crystals. Can be bought in bulk online or in craft stores. If you're lucky you can get them in a gardening shop. Drying time: 5 days
- A mix of equal parts of borax and cornmeal in a bowl and add 2 - 3 tablespoons of non-iodized salt per quart of mix. (source: eHow) Drying time: 5 - 15 days (needs to be checked every few days).
- Dry fine sand. I suggest using the kind sold for bird cages. Sift the sand and make sure it's completely dry. Drying time: varies (has to be checked every few days)
Remove all leaves from the stem. Take a big plastic or paper cup and a knife with a sharp point and cut a little X into the center of the bottom. Push the stem through that slit until all of the flower head is inside the cup plus half an inch / 2 cm free room on top. Then slowly pour your desiccant into the side of the cup (not directly on the flower) and let it pile up around the flower. Once the desiccant surrounds the flower head, gently sprinkle desiccant directly over the flower head until it's entirely covered. Let it sit that way for the time required by your desiccant.
Drying with a desiccant can make the flowers extremely delicate and brittle and you must be utterly careful and gently whenever handling it.
After the rose is completely dried, you could put it in a high glass display dome like this type (Link to image source and shop. I'm not affiliated in any way. This is just one of many examples of flower display domes):
Or you could embed it in epoxy resin. However my personal experience with epoxy to preserve valuable items is that you might be disappointed. You have exactly one try to make it right. If it doesn't work, you could try again with another rose, but it will never be that special rose again.
- Epoxy will yellow after some time. Low quality, cheap epoxies can yellow immediately, high quality ones will do after some months in direct sunlight or after some years kept out of direct sunlight.
- Without a vacuum chamber it's impossible not to trap air bubbles between the flower petals.
- Epoxy does change the color of dried flowers. Red color will be bleached and white will get a yellow or brown tint.