I recently took a short course in making sugar flowers at my local adult education college. We learnt how to make carnations, lillies, sweet peas and roses (about the ninth time I've done roses on a cake decorating course!) and also watched a demonstration of how to make frangipane. In the last class we could make whatever we wanted from the past few weeks to create our own bouquet.
It's amazing how different the techniques are for making different flowers and how much they do actually look like the real thing! For the carnations, we had to buy a carnation cutter; you can get them from cake decorating shops (online or in person) though I got mine from Amazon. You need to make sure you get ones with more detail around the edges as this helps make the flowers more realistic.
To begin you need to make the centre of the flower that the petals will go around. Take a length of florist wire, about 26 or 28 gauge (the higher the number, the thinner it is) and cut into three pieces. Take a small amount of flower paste in the colour you are going to make your flower, and one double-ended flower stamen (again you can buy all this from cake decorating shops or Amazon; I picked up a lot of supplies when I went to the Cake International cake show a few years back).
Using pliers bend the end of the wire into a tiny hook, and thread the stamen through it so both ends are pointing upright. Take a tiny ball of flower paste, wrap around the bottom of the stamen and leave to dry.
Roll out some flower paste very thinly and use the cutter to cut out one petal (do one at a time or they will go dry; cover your flower paste in clingfilm or put it in an airtight bag while you are not using it).
Use a friller tool or ball tool to curl the edges of each part of the petal. Rest it on a foam pad to do this - a hard surface won't work.
Push the wire through the petal and bring the petal up to the top to meet the centre and stamen, and fold the petal in half.
Wrap one side of the petal in towards the centre and wrap the other side of the petal outwards so it looks something like this:
Repeat the process by cutting out a petal, frilling the edges and pushing through the wire. Don't fold this one though - sit it behind the petal you've already added and shape it upwards slightly.
We also made a green calyx - the leaves that are attached to the bottom of the flower. You can buy a calyx cutter in different sizes or cut out the shape yourself freehand.
You need a small ball or raised part in the centre as you can see here:
Push the wire through so the calyx sits under the flower and curl the edges. Finally snip off the excess stamen so they don't stick too far out of the flower.