Download an audio file of a native Dutch speaker pronouncing the letters in the Dutch alphabet. There are a number of language-specific websites that offer audio clips of pronunciation of individual letters in the Dutch language, and Dutchgrammar.com has an audio file available for download that features a full reading of the Dutch alphabet.
Listen to the alphabet pronunciation on a portable mp3 player on your commute or during off hours. Many of the letters in the Dutch language are pronounced the same as they are in English, so grasping the differences and memorizing the sound of each letter shouldn't take too long.
Write down each letter of the alphabet on an index card. Shuffle through them to quiz yourself on pronunciation. There is scientific evidence that people learn faster when using a rewards system, so give yourself a small reward for every 10 letters that you identify correctly in a row.
Sing the Dutch version of the alphabet song to keep the pronunciation firmly rooted in your mind. Use the same tune and the English version but substitute Dutch pronunciation for each letter.
Play a memory game with friends or family members who are also learning the Dutch alphabet. Shuffle your index cards and set them in a pile between you, face down. Flip them over one by one and see who can say the correct pronunciation first; award a point for each letter identified first.