I started out drawing a tear shape on paper and cut it out to use as a pattern for the petals. The shape can vary, round, oval or heart shaped for example. I made five petals, but you can have more- if your felt is on the thinner side, then perhaps you have to, to fill up the flower.
Then I pinched the petal at the rounded end so it folded in the middle and stuck the needle through, perhaps 3 mm from the end.
String the rest of the petals after the first.
Now comes the trickiest part. Put the needle through the first petal again and pull tight, so the petals form a circle. Do it slowly and arrange the petals to your liking as you go. When you have got the shape right, then go through all the petals one or two times to make the flower more stable and secure the thread. Done!
I made a second flower, as you can see, made of completely round petals. For a finishing touch, sew a pearl or two or more in the middle. Or glue a small circle of contrasting felt there. If you want to mount the flower on a pin or clip, then I think it is a good idea to stitch it to a felt circle first, for stability. I mounted my flowers on clips, which I found in the jewelry-making section of a hobby store. If possible, try to get clips with small holes so you can sew the flowers to it, though I suppose that it would be possible to use glue as well.
I hope you found this helpful and not too obscure! If you make a flower, I'd love to see the result!