Attach the rug carefully, especially if it is an expensive rug. You may use push pins or brads but this is only a temporary method. Use it to hang the rug in various spots until you find the ideal showplace.
A more permanent solution is to use Velcro, which can be stitched on the back of the rug. The soft part goes on the rug. Attach the firmer side to a wooden board. Line the rug on all 4 sides and put at least 2 large strips of Velcro down the center of the rug. Use enough Velcro to support the weight of the rug. on the wall.
Stretch the rug and mount it on a wooden frame or painted plywood by using a stapler or tacks. This will work well for a heavy rug, but the staples may show. If you use tacks, match them to the color of the rug or choose colors that complement the rug.