My concrete driveway and patio have sunken slightly and water puddles when it rains. There are a number of cement products that can be used from plain old concrete mix to special Portland cement mixtures that can be applied as an almost paper-thin coating over existing work. There are a few preparatory steps you should follow to assure the best adhesion of these products. First, the surface of the old work should be cleaned and roughened slightly.
Concrete becomes harder and less porous as it ages.
Chemical concrete cleaners containing phosphoric acid will both clean and slightly etch the surface and increase adhesion between the new and old work. The use of muriatic acid, a more powerful acid, is more efficient but much more dangerous to use. You can decide for yourself if you want to work with this product. This would require the rental of special power tools or a sand blasting equipment. Generally speaking, the chemical method is more economical for small jobs such as small sections of a patio or a cement walk.