If you're carpentry-inclined, build your own furniture. Look online and in books for instructional guides, which are readily available for practically every piece of patio furniture you could want: tables, coffee tables, chairs, benches and hammocks. Building the furniture allows you the freedom to customize it: for a concrete patio, you could incorporate soft textiles into the furniture for balance, such as tablecloths, table runners, seat cushions and accent pillows. Be sure to purchase material suitable for outdoor use. Another bonus is that furniture made by you has sentimental value.
Check with friends, neighbors, co-workers and family members for any outdoor furniture you could have. Secondhand furniture may be marred by minor damage here and there, and if you get pieces from several sources, they may be mismatched; but there are ways around these problems. Sand out scratches, then redo finishes to hide cosmetic flaws. Cover a stained or discolored tabletop with a tablecloth. Reinforce rickety chair and table legs by installing braces. To make mismatched pieces uniform, spray paint all wooden or plastic furniture with the same color and buy complementary slipcovers and re-cover every seat cushion with the same fabric.
Concrete patios may sometimes be missing natural elements, so consider this in your decorating plans. If greenery is lacking, bring in potted trees, plants in pots and planter box/benches, even whole container gardens. Add decorative stones or large boulders that could provide seating. A water fountain adds the restful sound of splashing water. Use a fire pit or a chimenea, a portable, freestanding fireplace, to add the drama and ambience of fire.