There aren't many reasons to have only a 1-inch thick concrete surface. It is too thin to use as a flooring just by itself; however if you need to resurface damaged concrete, a 1-inch layer is a good amount. The old surface is prepared so that the new concrete will adhere, then the new cement is added. You will need a frame to hold the mix until it hardens.
Build a frame for your concrete. Build it around the damaged concrete so that 1 inch of the wood extends above the old concrete. Measure around the old concrete and cut boards with a power saw to fit. Drill the boards together with 2-inch screws.
Drill stakes into the outside edge of the boards with more 2-inch screws. Hammer the frame into the ground until only 1 inch of wood is above the old concrete.
Mix up a concrete overlay using 2-1/2 parts sand and 1 part portland cement. Add water to the mix until it is the a consistency of a thick wet mud. It doesn't need to be thin enough to pour like a liquid, but not so thick that it clings to a trowel. A thick milkshake is a good example.
Dump the cement in the frame and spread it out with a trowel. At this time you can leave it as is to dry. Of if you would like to add to the surface, you can stamp it. You must wait to stamp until the surface will retain an indention. Put your fingers into the surface to test it. If it remains, then you can proceed with the stamping. Stamping requires a concrete releaser be sprayed so that you can remove the stamps after setting them in the cement. Place the stamp forms in and press them down. Repeat to cover the area.