Antique buttons are collectibles and may have a market value beyond what you might imagine. There are a number of different ways to sell your antique buttons, but before you start selling, you need to do a little research on their present day value. Once you have done that, then you can get to selling.
An inexpensive option for doing your research is your local public library. You can borrow books for a period of time, or consult the reference section, which every library has. This area contains books that can't be borrowed but are great for looking up information. Library staff can assist you in finding books on antique appraisal values. You can take photocopies of the pages that you're interested in for a minimal cost.
Take your buttons to a local antique dealer to have them appraised. Ask first if there is a charge for this service. A hefty appraisal charge may be more than the items are actually worth.
Specialty and even secondhand bookstores may have books that list antique and collectible items and their current values. Even if the book is out of date, it will at least give you a guide for the value at the time of printing.
Take digital photos of your items on a dark background from two to three viewpoints. Be sure the items are easy to see and look as attractive as possible.
Selling online to others who are interested in your items is a fairly inexpensive way to give your items huge exposure to potential customers. You'll need to write up a brief description of the buttons and post the photos you have taken. EBay and other online selling sites are an excellent place to start. Signup is easy, costs are minimal and exposure to your items is high. There are many online sites that specifically buy and sell antique items. If you do a search for the items you have, you'll see if others are selling them and approximately what price they are going for.
Antique dealers and secondhand stores usually work on commission. They may be interested in taking your items, displaying and selling them for you for a small cut of the selling price.