Great question! Homes that are listed as "open to inquiries" are ones where the host has not indicated that their home is available, nor have they requested a swap to your area. You're welcome to reach out by clicking "send a message." This will allow you to send them a message and allow them to start a chat with you if they are interested. You'll see the option to send a message on their profile if they're open to receiving these types of requests.
If you and the host agree on dates, the host can open their calendar to you right from the chat so you can request them. Only you will be able to request dates outside their posted availability, and the host still decides whether to accept your request.