Learn the basics of Kenjutsu. The Arts of Fight, in Resources, has a good rundown of the martial art, and you can use the website to learn some background information regarding Kenjutsu. This teaches you about the differences between Kenjutsu and other similar martial arts, such as Iaido.
Get a bokken. The bokken is a wooden training sword, but it can also be regarded as a weapon in its own right. The bokken is an invaluable tool during your training, a safe way to practice the techniques that you learn. Be careful during your practice, because though a bokken may not be able to cut anybody, a full strike with one can easily break bones.
Study the basic parts of the sword. Understanding the names for the various parts of the sword is important because they are referred to by those names in online material. See Resources for a diagram with sword names listed.
Learn how to correctly hold the sword. The sword is held with two hands, with the dominant hand closest to the hand-guard. Your dominant hand is used to balance the sword, and your weaker hand should hold the sword close to the bottom of the handle. There should be a space between your hands to allow for better maneuverability. Beginners can benefit from holding the sword with the index finger extended, as this should not be used to help grip the sword. Try to grip the sword loosely. See Resources for more information.
Learn some basic Kenjutsu strikes. After you have mastered holding the sword and you understand the basics of Kenjutsu, learning a few strikes is the next step in learning online. The Shinobi Kai Scroll on Ken No Jutsu Tony details a few basic strikes. There is a combination of in-text descriptions and videos to teach you the techniques.
Study online videos that teach Kenjutsu techniques. Fight Authority, in Resources, is one website that hosts a lot of instructional videos, and is a useful resource as you continue your study. Finding good sources about Kenjutsu can be difficult, so consider investing in some instructional books or DVDs to continue your study.