Base shoe is like a crown molding in my opinion. There will be a lot of 30 or 45 degree cut to make corners look a lot of nicer. Thus, Miter Saw will be a nice fit for this project. I was using this less power tool borrowed from my colleague Po(thanks). This is an awesome tool because it does do the job very nicely.
In addition to the saw, I also need a nail gun to save time. Using hammer is not only time consuming but also error prone. I highly recommend to use a nail gun instead. There two kinds of nail gun. Air-compressed nail gun is much powerful, but you will need to purchase a separated air compressor. Electric nail gun is less powerful, but for this kind of project it is sufficient.

We will also need paint and brush for the final finish.
Everything is ready, now let's begin.
Step 1: Measure the width and cut the base shoe roughly.
Step 2: Cut 45 degree angle for the corner. Some corners require 30 degree angle which will take more efforts.
Step 3: Drive the nail to the base shoe and wall. This will close the gap shown in the picture.
Step 4: Brush the paint to give it the final touch.
Reference:
1. http://www.ehow.com/videos-on_4990_install-base-shoe-molding.html