I am going to assume you have a single bird, as with two.... it is monkey see monkey do and is much easier.
1. Pick veggies high in Vitamin A as your main fresh feeding goal. Those that are red, orange and yellow are generally highest in Vit A.
2. Pick a cut size and stick with it for at least TEN different introductions. Shredding on a box shredder, julienne, or mince is a good size to start with for a Bourke or similar sized parrot. If they have never had any fresh, start with a piece of kale to start as that is easy. Then move to a few kernels of corn that were from a frozen bag, warmed and tossed in egg food or Miracle Meal is a good first bite. If they go for that, move on to another veggie as corn is higher in sugar than we like to offer more than a treat sized amount.
3. Use a bowl familiar to them for food, that way they aren't adjusting to the new bowl and the new food at the same time.
4. You can remove all food from the cage the evening before so they are good and hungry. That helps.
5. Patience! It can take a while, but it is so rewarding to see them eating a healthy diet that also offers them mental stimulation along with nutrition.
--- Other thoughts: Try sprouts, those are nutritious and more like a similar food that they are likely to try easily. Be sure to take fresh out of the cage after a couple/few hours depending on ambient temp. Stainless kabobs are a good way to use larger pieces in a toy like setting that may get them pecking! Be sure to steam or par cook sweet potatoes.
Good Luck! Keep us posted!