How can I drain water from the area between a concrete walkway and the side of the house?
As other's have mentioned in comments, having the walkway sloped properly may reduce the problem.  However, if the area between the walkway and the house is lower than the walkway, you'll still likely end up with water trapped there. 

The most common solution to this problem, is to build up the land between the walkway and house. Most folks us the area as a flower bed, and build the dirt up higher than the walkway. The raised land should shed most of the water away from the house, and eliminate the puddling problem you're having.

If you don't like flowers, you could raise the land a bit and plant grass instead. The key to solving the problem, is to have the land raised higher than the walkway. 

If you really want the land to be lower, you can install a french drain or other drainage system. This will allow the water to be moved away from this area, though will most likely involve tunneling under the walkway (or ripping up a small section) to run the pipe.