What is the easiest way to get wrinkles and deep creases out of new curtains?

Spray them with water should work and then just let them hang. You could steam them if you have a steamer, that would even work better, just be careful not to hold the steam handle too close because of the heat. If they aren’t very large you could get them damp and tumble dry them on a low temp for a bit, just double check the wash instructions if you decide to do that, don’t just go by my suggestion. I would do my first suggestion first if it was me. It’s the simplest, and if it works you’re done.

How big are they? Can you hang them in the bathroom for a few days and let the steam from showers gently loosen the creases?