A spell, simply put, is any action designed to harness
natural energy and put it to use in getting a desired
result. There are many, many ways to "cast" a spell, but there are some things you should understand about
casting spells before you attempt to cast one.
FIRST AND FOREMOST, you should seriously consider obeying the Rede and remembering the Threefold Law. You should never attempt any spell that will hurt someone else, and furthermore you should try to specifically focus during your spell on making sure that your result comes about without causing anyone harm. Most people won't cast a spell involving someone else without their permission or unless permission is understood. That's why "love spells" are out of the question. You should never try to "make" anyone feel something they wouldn't want to, or make anything happen that is against Nature; not only will it probably not work, but if it has any effect, it will just confuse or hurt the person, and probably their natural inclinations will take over if they ever strayed at all.
Spells make use of the forces already in motion and do their best to encourage change. The planet's daily, monthly, and yearly cycles must be incorporated into spells. Magick (spelled with a 'k' to distinguish it from what stage magicians do) is not really "otherworldly" because it is natural. Using it often requires a slight (or sometimes great) shift of consciousness, but it is completely of this realm and possible for everyone. No tools are necessary and spells do not have to be cast as large productions. A spell can be as simple as concentrating on wishing that someone will call you or dream about you; you don't have to light any candles to do it or anything like that, since every spell starts with your mind and can be finished with only your mind as well. Everything else is an extension, and sometimes a useful extension; some people have more trouble than others shifting their consciousness or focusing energy. But even if you don't have trouble with these things, doing a spell with tools and other special, more elaborate practices can increase effectiveness.
Through tools, concentration, energy-raising, and lots of practice, we can learn to set things in motion with the natural energy we all have, making the best of our position in the cycle and the universe. We can use spells to ask for blessings, to help other people, to lead us to increased knowledge, and a number of other things. That's all it is; it's no big mystery, it's not really "occult," we don't have "special powers" (any more than anyone could), and it's not anything evil, crazy, or even strange. Magick works because we believe and because we can successfully manipulate symbols and energies to open the channels we desire.