Before using any concrete filler, make sure there's no oil or dirt still on the floor. If there is, use a cleaner that cuts grease. This will help the filler bond to the cement.
Use a cold chisel and a hammer to get rid of any large pieces in the crack. Hold the chisel at an angle and pound with the hammer to chisel out the crack. This is called "keying" the hole to make the base or inside of the crack bigger than it is at the surface. Keying helps the new patching material bond with the old crack.
To use the concrete filler, cut the nozzle off the bottle and slowly fill the cracks (image 1). If you're using mixed concrete patch, mix according to the manufacturer's direction and then trowel the patch into the crack (image 2). Check the cracks in a few minutes to see whether the filler has settled. You may have to add some more if it doesn't look tight. Use a trowel to smooth out the cracks
Allow the filler to cure overnight or at least the duration recommended by the manufacturer. Then check it again to see if any additional patch is needed.
After patching the concrete, it's a good idea to seal it. Concrete easily absorbs stains, and sealing will prevent that. There are more than a few products available for concrete sealing, but a heavy-duty water-based polyurethane is a good choice. If the floor has a rough finish, apply the polyurethane with a broom or brush using the bristles to work the sealer into the rough surface. With a smooth surface use a roller.
The beauty of water-based polyurethane is that it dries quickly, so you can put on a second coat just a few hours after the first. Also, water-based polyurethanes don't smell as bad as other types of sealer. In heavy traffic areas, it's a good idea to apply three or four coats.