Personally, I grew up with it, so believing in magick wasn't something I struggled with. I would suggest checking out witchvox.com and maybe visiting an event such as a Sabbat gathering (Beltaine is May 1st) so you can witness it first hand. If you're unable to do that, then the next possible way to "believe" is just learning all you can about it. There is a book called the un-spell book that is one person's opinion on how magick works, it may help you to gain an understanding of it. http://www.llewellyn.com/product_browse_inside.php?ean=9780738723389
This author also wrote another one previous to this that is also a beginner's guide. I've flipped through the Un-Spell Book before and it looked like it was well written and thought out.
You don't really need belief in "magick" just yourself. The placebo effect, mind over matter, etc are all scientifically documented facts. The mind is a powerful thing and can perform amazing things. Your mind is the key to making magick work, so believing in your own abilities is important.
I remember as a kid, I would put my hand in hot water and force myself to believe it was cold. And vice versa, put my hand in chilled water and force myself to believe it was hot. I did it because even at a young age, I realized that I could change my own perceptions. I can't remember what provoked me to do this. When I began to practice magick, I took the same concept of focus and will and applied it. If you try this just make sure you don't put your hand in for too long or make the water too hot or cold (I used water from the tap)! Just because you may make yourself believe it isn't hot or cold doesn't mean it can't hurt you.
When I began to seriously practice magick, I was already confidant in my own mind. It helped of course that I also had a mother and aunt that practiced, and I witnessed some of their work. They also let me feel the energy off of their hands.