Demolish and remove the existing sidewalk to make room for the replacement.
Dig down far enough to lay a 4 inch layer of gravel, followed by a 2 inch layer of sand and a minimum of a 4 inch layer of concrete.
Line the trench with inexpensive hardboard to create the edges for your sidewalk.
Make sure the bottom of the trench is level and lay the 4 inches of gravel. Lay the sand on top of it, water lightly and tamp tightly with either a compactor or a flat board nailed to a 2 by 4.
Pour your concrete and use a float to work it level by pulling a spare 2 by 4 across the hardboard. This will pull the concrete into areas and create a level surface.
Trowel the concrete smooth. Be sure not to overwork the concrete as this point, as it will weaken the end result of your walkway.
Broom over the top of the concrete to create a surface that is not dangerously slick.