Filing form I-130 for parents. Received notice of approval. What's next?

Since they're back home, the petition will be sent to the National Visa Center, and you'll be contacted and asked to provide I-864 affidavits of support for them, plus a fee to process them. It can take an additional 6 months to process them, depending on how long it takes you to respond and whether or not you get the forms right the first time. From there, it will go to the US emby or consulate where they live.