Contact or visit your local DVD rental store. They will have a list of new movie DVD release dates for at least the upcoming month. The list is usually posted. If you don't see the list, ask a customer service rep. They often know what is coming in to their store a month before it hits the shelves. Often older movies will be recorded on DVD and get released without any notice as soon as they are ready for shipping.
Visit the popular electronic chain stores and their websites for their new movie DVD release dates. These stores sell many of the movies the first week on a discount sale and will have lists of release dates available to the public.
List the name of the DVD movie at the top of your rental queue if you want to receive it ASAP from your mail rental company. If you subscribe to a mail DVD rental company, you must have the movie in the top of your queue and have sent back at least one of your already viewed DVDs. Time it so they have your returned movie by Monday and can send the newly-released DVD so you can get it on Tuesday or Wednesday.
Browse the Sunday ads in the newspaper for DVD release dates. This not only will show the sales price, but what is coming out the upcoming week. What is coming available for sale is usually what is available for rent.
Order the movie you want online. If the website that you are ordering from can process the order, they can get it to you the day that it is released. Stores and rental companies get the DVDs days in advance so they can process them.