Here is a basic recipe. This is one that can be improvised.
Here is a more elaborate recipe.
A few basics: Use the best rice you can get. A short grained risotto rice like Aborio is what you want. In a pinch do not let perfect be the enemy of good: You can use any short grain rice. Asian sticky rice will work well.
For Christmas Eve it is typically done vegetarian, although I would not leave out cheese and butter (and egg is essential). I typically prepare the rice with real saffron, let it cool completely (I usually prepare about a pound, dry, the night before so it can get cold). Then, just before cooking, I add egg yokes to the rice I am going to cook right then, along with grated mozzarella and Romano cheese. I mold rice balls and then dip them in the egg whites, followed by rolling the balls in Italian bread crumbs (seasoned or unseasoned, your choice).
When I have a plate full, I fry them in hot grape seed or peanut oil, until crispy brown as shown above. Then they are transferred to the oven. You can season the rice anyway you want. Try different types of cheeses and seasoning. The rice is essentially an empty canvas (the saffron just lightly seasons it). Personally, I like arancini simple (some like to dip these in marinara sauce, but I like them as shown above). You want to make these in small batches and serve while hot.