Visit one of the pet friendly hotel search engines available on the web. Three of them are Pets Welcome, Dog Friendly and Pet Travel.
Choose your destination. Most of the pet oriented search engines will ask you what city, state and country you would like to visit and return area-specific results for that location. Review the policies and fees.
Make your selection and book the room. Some of the search engines allow you to book directly from their websites, while others simply provide the property information so you can book directly with the hotel. In either case, once you have the name and location of the hotel you would like to stay at, you can contact them directly to confirm their pet policies and book your room.