Where to Start
You will quickly notice that the areas that require the most cleaning are usually those that are highest traffic. The main areas to consider are the rooms/areas where the front and back door are.
You can use either a small dust broom with the accompanying pan or your vacuum if it has a small brush attachment.
Whatever option you choose, make your way around the room methodically brushing or vacuuming the baseboards from the top to bottom. You will notice that the majority of dust will collect at the top of the boards.
If you are dusting with the broom, hold the dust pan at floor level and catch the dust as you brush it off. When vacuuming you will not have to do this as all the dust will be collected by the vacuum.
Take a clean old t-shirt or cloth and soak it in clean water. Wring the cloth and use it to thoroughly wipe down all the baseboards. Soak, wring and wipe as required until all the baseboards in the room are wiped clean.
Keep It Up
A clean house will not require that baseboards be cleaned more often that 2-3 times a year, however it is a good habit and practice to keep in mind. As a parent, it is also a wonderful way to set an example for kids or get them involved in cleaning on a small scale (allowance included)