Slate has been a popular building material for centuries, used often as paving and on buildings for roofing. It's hard, tough, durable, colourful and because of its nature can be sliced thin or cut into regular shapes easily. Slate is heavy and transportation costs once severely limited its use mainly to areas close to quarries or supplies. Today it is readily available in most locales, although prices may vary widely. You can install slate in a garden as individual stepping stones or in paths and walks, using either irregular stones or tiles cut in regular forms.
Lay out a garden path with stakes and builder's twine or for individual stepping stones with a garden hose to mark the alignment. Set individual stones in position to cut out sod or soil around them. Mark borders for a regular walkway with metal or plastic edging on both sides. Decide whether you want to set the stones in sand or in mortar; either works but sand is easier and more adjustable.
Dig out the slate area with a spade. Dig individual holes around the outlines of the stones for stepping stones or dig the width of the path. Remove all the sod and dirt the depth of the slate plus about 3 inches to set individual stones in sand or about 6 inches for a formal walk to allow for a gravel base topped with a sand bed. Smooth the sand roughly level so its depth is approximately the thickness of the slate.
Set individual stones in the sand bed and level each one with a level. Tap the slate firmly into place with a rubber mallet. Lay a slate walk by setting stones in the sand bed in any desired pattern. Place irregularly shaped stones with a mixture of sizes to go side to side and end to end. Install regular stones in a pattern; you can use a straight bond, with joints aligned, a running bond, with joints overlapping or some other pattern like a herringbone, with rectangles formed in L-shaped patterns. Tap stones in place with a mallet and level them.
Fill dirt or sod around individual stones to secure them. Sweep fine sand or stone dust into the joints of a full walk; slate dust is ideal if available. Repeat the sweeping until all joints are filed completely. Remove the edging or leave it in place as a grass barrier.