Prepare the cement walkway for the flagstone. Remove broken pieces of slab, brush off debris and use a level to ensure that the cement sections are flat and even. While it's recommended that you lay a 4-to-6-inch base layer of pea gravel or sand beneath your flagstone path, do-it-yourselfers laying flagstone over cement generally skip this step.
Fill in low areas or areas where broken pieces of cement mar the smooth and level surfaces. Dig around the side of the cement slab and push dirt or sand beneath to create a level surface. Fill broken areas with cement or thinset and allow them to dry according to package instructions.
Design a rough layout for your flagstone pieces by setting them on the cement walkway to get an idea of where to place the stones before you start. Choose the topside of your stones for visual appeal and smoothness. This not only helps to create visual appeal but also reduces the chance of stubbed toes, trips or accidents when the job is completed.
Trim or break stones as needed with a mortar hammer or a circular saw so they don't hang over the walkway's edge, and to offer a better overall fit.
Work in manageable sections--usually a 3-by-3 or 4-by-4-foot area--to lay down a layer of mortar for your flagstone base. Thick or large chunks of flagstone may need a deeper layer of mortar than smaller pieces, so adapt accordingly. At least one-quarter of the flagstone should be buried or settled into the mortar for a solid and permanent fit.
Tap the stone gently into place using a rubber mallet. Place a level on the stone to ensure an even plane.
Fill in cracks or spaces between stones using either small gravel or mortar, depending on the look you're going for. When filling cracks with mortar, apply it liberally, then use your float to scrape off any excess. Allow the mortar to dry for 10 to 15 minutes, depending on the ambient temperature, then dip the float or a rag in water and clean surface of the flagstones. You may need to repeat this process several times until the gray film caused by the mortar is gone.