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Adding a layer of cement to your driveway and/or patio is one option. 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. There is an article at the website on muriatic acid at https://www.naturalhandyman.com/iip/infxtra/infmur.html. You can decide for yourself if you want to work with this product.
If you prefer not to use these chemicals at all, you can mechanically roughen or "abrade" the surface instead. 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. On the other hand the mechanical method is better for interior work (no chemical fumes) and large surfaces, such as driveways and patios. You should still clean the concrete with a detergent of some type. TSP or a TSP-substitute (for those of you living in TSP-free zones) are fine choices.
After the surface is cleaned and abraded, it should then be soaked with water until it is completely saturated. This step prevents the old work from absorbing the water from the new cement which can cause a "dry" spot where the two meet, producing a weak bond. The concrete should be damp when applying the patching material, but all standing water should be brushed or wiped off.
One step that many of the packaged mixes don't include is what I call "priming" the concrete. After dampening the concrete surface, mix a cement "slurry"… a somewhat thinner-than-usual-mix of the patching compound… and brush it into the concrete surface with a stiff-bristle brush immediately prior to applying the patching material… don't let it dry out! This step helps the old and new work bond by mechanically forcing the cement into the minute cracks and crevices of the old work. This step is not absolutely necessary, but it can't hurt!
Many hardware stores sell liquid chemical additives that are added to the mix to help new concrete bond to old work. They also add some extra water and crack resistance to the concrete. These products are wonderful and you should definitely add some if you use a plain concrete mix for your repair. However, if you purchase a cement product designed for patching applications or for thin coatings, don't use any of these additives.
If you need to build up the concrete more than an inch but for leveling purposes to taper the patch into the old work, you may have to do two pours with different cement mixes. The reason for this is that cement mixes have different aggregates… sand or stones that add strength and act as fillers to reduce the cost of the product. The smaller the aggregate size, the thinner the cement can be poured. For example, concrete mix (also known as gravel mix) has large aggregate and cannot be successfully poured thinner than a half inch to an inch. On the other hand, so-called "topping" or resurfacing mixes with very fine aggregate can be applied in thicknesses from under an inch to a feathered-edge. So the method for a tapered pour is to first pour the concrete mix to at least a half inch below the final desired level. It does not have to troweled smooth. In fact, a little roughness in the first pour helps the second pour to grab more effectively! Let the cement set for a few hours and then do a second pour with the resurfacing or patching mix, feathering it into the old work.
There is an alternative to resurfacing you might want to investigate. There are methods that can be used to raise a sunken slab of virtually any size back to it's original position. A number of companies specialize in "concrete injection"… a process where a special mixture of cement is injected under pressure underneath the slab, essentially floating the slab back into position. This process is also used to change the slope of a slab that is directing rain water the wrong way… like towards your foundation! These companies have some interesting names for their repair techniques, too… "slabjacking" and "mudjacking" are two that come to mind!
You might be able to raise the slab yourself… if it is not too large and
heavy. You can use a pick or mattock… a type of pick with one broad, flat end
used for prying or digging… to raise the slab high enough to add a filler
material beneath it. Various materials can be used. Sand is the easiest to work
with, though small stones or gravel are also acceptable options. You can also
use concrete provided it doesn't get squeezed out by the pressure of the slab.
Place a sheet of plastic under the slab over the wet concrete before lowering
the slab. This will keep the new cement from sticking to the slab… just in
case you have to relevel it sometime in the future.
Some long slabs, such as those used for concrete walks, are made in a single pour. They usually have expansion grooves cut into them at regular intervals to give the concrete a place to break neatly if stressed instead of cracking randomly. You can manually chisel out these grooves to separate a long slab into smaller pieces for lifting. However, if the slab is reinforced with a steel mesh or iron bars, this will not work.
Of course, a less laborious fix is to add a leveling layer of cement on top of the old slab... bringing us back around to the beginning of this question. Amazing how I always end up back at the "easiest" way to do a job. Again you get to benefit from my lazier side!