Sadly, if you have a spinning petal there is nothing you can do to fix it. So making making them right the 1st time is essential!
First, you need to make sure you are using the right kind of wire - paper wrapped is the best, cloth is decent.
Make sure you are using the right gauge wire for the job. Not too fat, not too thin.
You need to make sure you roll your paste where it's thicker at the end you are putting in the wire.
Make sure you use a gum glue. Dip your wire in, dab it off then insert.
Veining not only adds a natural element to your petals, but it also helps the wire attach. If you are making simple orchids you can use a Viva paper towel - roll your petal, add wire, then lightly press it between 2 Vivas that have been dusted in corn starch. Apply more pressure where your wire is. It adds a slight realistic texture and will help your wires attach.
Set them to dry and leave them alone. I wait a minimum 24 hours before I start messing with my petals.
Aaaaand the type of paste you are trying to use makes all the difference in the world. I highly recommend making your own using Nicholas Lodge's recipe (google it).
Hope this helps!