Visit the book author's website. Oftentimes authors will sell promotional materials through their own personal website that you can purchase by way of credit or debit card and have shipped out to you.
Visit the book publisher's website. You can typically find the publisher of a book and their online information within the first few pages of a book. Publishing houses typically feature a "store" section on their website through which you can buy physical copies of the book and promotional materials.
Email the publisher if you are unable to find the poster that you are looking for on their website. Often an employee of the house can look into its availability and direct you to a place of purchase.
Go to your local bookstore. Small book shops and major chains alike often house many promotional posters. Ask a store employee if the poster in question is available, and if so, if you could have or purchase one. Once a poster is no longer in use, often stores can give them away to free up space.
Go online to auction and retail sites such as eBay and Etsy. People and shops that no longer need these posters will often post them online. If the poster is a collector's item, you may be able to purchase it in mint condition.