There really is no style of home decorating that can be identified as decidedly Native American. There are however touches that can be added to almost any style of décor. The trick is always a matter of incorporating these things without making them seem out of place. Of all the design styles that exist, and of course depending on the tribe in question, the southwestern style of home decorating and design would actually make a good match for many Native American artifacts, touches, and artwork.
Pottery is central to a Native American theme. Different tribes had different styles of creating pottery. If you have a favorite tribe or a favorite style of pottery you may want to build the remainder of the room or design area around the pottery you love as it is quite personal to many people and not all styles of pottery will match all other styles of weaving, carving, basket making, or artwork. Pottery is very useful in a kitchen if you plan to use some of it in this room. Not only can most pottery be baked when cooking but it also works wonders for storing things like utensils that you would like to have in reach, strays, napkins, and any other things you can think to store within the pottery you have available. If you are going to pay for it you may as well put it to good use.
Speaking of artwork. There are some beautiful Native American prints as well as some 'sand art' that is a must have for a room that is trying to capture the spirit of the Native American or at least a specific tribe and incorporate that spirit into their homes. I think this is a beautiful idea for those who wish to pay their respects to those who are ancestors to many of us. Not that the pottery mentioned above isn't art work in and of itself but the addition of art that can be placed on the wall is a welcome addition in many homes.
Keep in mind also that many Native Americans played the flute. Some people display a collection of Native American flutes next to their prized pieces of art. There really is no wrong way to go about home decorating when it is your own home that is being decorated. Select the things you like, omit the things you do not like. You do not even have to be loyal to one tripe, design, style, or region when decorating your home. Some people have happy little collections that are filled with all kinds of odds and ends pieces from a wide variety of artistic styles along the way.
For those who are hoping to stick with a somewhat Native American theme baskets are once again a good selection to add to the collection. Baskets are not only lovely but also incredibly useful for holding blankets, throws, rugs, pillows, knitting supplies, magazines, and anything else you do not wish to have cluttering the living spaces of your home. They are even quite good about hiding remote controls for the electronic equipment when you place them cleverly throughout the room.
The best suggestion for those who wish to honor their Native American neighbors and ancestors by incorporating the artwork and designs into their home decorating plans is not to spend too much time planning. The Native Americans appreciated nature and allowing many things to happen naturally. Use this opportunity to learn this very important lesson while incorporating other great things you appreciate about them into your home.