water drainage WHEN IT RAINS
The best way to raise a side walk of the type you describe is to remove the old one by breaking up the old one and hauling away the old material. 

Then you prepare the base area with new fill to build up to the level needed. Note that it may be required to even replace some of the old base material if it was not properly prepared under the original sidewalk. One thing to look for is organics in the soil that can decompose over time leading to voids in the fill.

Finally the time comes to build the forms for the new sidewalk to define the size and top level of the replacement sidewalk. Before filling the forms with new concrete make sure to think about adding suitable wire mesh and/or rebar.

Try to avoid the short cut of just adding a few inches of concrete on top of the old sidewalk. The problem with doing this is that it does not last a long time, especially in areas with freezing weather. Water can seep into the joint area between the two layers. When it freezes it expands and can push the layers apart and even cause the relatively thin top layer to crack.