There's nothing like having your cake decorating instructor inform you that her favorite flower is daffodils to inspire you to get them down. They are a bit tricky, but ultimately not too complicated. Here's the setup:
There are two bags of royal icing; one has been thinned slightly. The one that's regular thickness has a #104 rose tip, and the thinned one has a small round #2 tip (the instructor and the Wilton book recommend #1, but my icing was a little to thick to fit through that microscopic hole, even when it had been thinned with a few drops of water). Also on hand is a flower nail with a daffodil template decal, a glue stick, a #3 tip, a parchment paper square for each flower, and a dusting pouch filled with a 50/50 mix of powdered sugar and cornstarch. The first step is to attach a parchment square to the nail with a dab from the glue stick:
Then, holding the nail in one hand and the bag with the regular icing and the #104 tip, hold the wide end of the tip in the center of the nail. Line the tip up with one of those faint, dotted lines in between the heavy lines, and squeeze while moving the bag in an upside-down U sort of way, keeping the narrow end of the tip a couple millimeters above the surface.
This angle shows the perky way the edge of the petal should look:
Pipe five more just like it; tuck the tip under the petal to the left of it so that each new petal will be overlapped by the one you just piped next to it. Your bag will be almost level with the nail until the very end; pipe the final petal while holding the bag perpendicular to the nail; otherwise the tip will drag through the first petal:
Before the petals have a chance to dry (which they will do fairly quickly, being royal icing), touch the dusting pouch with your fingertips and gently pinch each petal into the classic daffodil shape; you may find you need to use the backs of your fingernails or other parts of your fingers to get in between the petals. As long as your fingers are coated in powdered sugar/cornstarch, they won't stick to the icing:
Here are all of the petals, after they've been pinched into shape:
Switch to the #3 tip, and pipe a small coil in the center of the flower. It should coil around 3 or 4 times. Try to make the first circle of the coil the smallest so the resulting coil is sort of vase-shaped.
Finally, pipe a tiny, zig-zag edge around the perimeter of the coil using the thinned icing and the #2 (or #1, if you can manage it) tip:
This versatile flower can also be a jonquil or a narcissus (my favorite flower) depending on the colors used and the size of rose petal tip (the jonquil is smaller, so is piped with a #103, for example). Experimentation WILL occur!