Here is the finished dandelion so you know what yours will look like. You'll need wire (22 gauge florist wire), needle nosed pliers, green wool, white wool roving, a felting needle, and a foam mat to felt on. Tomorrow I'll add some photos of other types of flowers made in the same way.
Start by making a wire form like the one below. I use a 22 gauge floral wire.
Wrap the wire with green wool. The ground can be a different color green or it can be the same as the stem. Felt the bottom part. You probably won't have to felt the stem, just wrap it tightly, pulling the last bit thin and continuing to wrap, even with just a few threads of wool. Do not wrap the loop on top!
Now comes the fun part! Take a thin "rope" of wool roving - it must be roving - and wind in through the loop over and over, leaving a finger's width of space. Sometimes I thread the wool through a large blunt sewing needle. It makes it easier to go through the wire loop.
Wrap the wool through the loop until it is full. Then you will pull all the loops up towards the top of the wire loop and, with your needle nosed pliers, pinch the wire closed. Your dandelion will look a little shaggy at this point.
Now it's time to clean it up a bit. Add more green to the stem so it is completely covered. Cut the loops with a sharp scissors and trim your dandelion down so it's more or less globe shaped. Don't overdo it. It's easy to see little uneven spots and keep trimming until there's nothing left!
Now you have a nice, neat flower that is ready for leaves. This I'm leaving more to you. I'm not sure my leaves look all that much like dandelion leaves. Anyway, you use the basic needle felting technique with a somewhat leaf shaped blob of wool and you work on it until it is shaped the way you want it - or until it's close enough to what you want. The next photo is a close-up of one of my leaves.