Read the instructions for the trick you want to perform. You can find instructions for a plethora of easy close-up magic tricks in the library, online or via a magic store. Before you get started, carefully read the instructions for the trick to glean any tips or cheats the magician who developed the trick has included for you.
Try to perform the trick slowly while following the instructions for the trick. Doing the trick slowly will allow you to analyze how the trick works and how you will best be able to manipulate your props.
Practice the trick in front of a mirror. Once you have the basic concepts and mechanics of the trick down, you will need to bring it up to speed. The best way to do this is to practice, practice, practice. Rehearsing in front of a mirror will allow you to see what it is the audience will be seeing and to correct any giveaways while amplifying your "magical behavior" in performing the trick. Part of magic is learning how to hide and obscure small movements, while amplifying others in flourishes or grand movements to misdirect the audience from what's actually going on.
Perform for an audience of friends and family. Ask them for feedback on the trick and what they think you can do to improve your performance.
If you're having trouble grasping a trick and/or would like some cheats and tips, a visit to the local magic shop will be valuable for you. Most employees of magic shops are magicians themselves, or are at least trained on how to manipulate the most basic tricks that the shop sells. They will be able to assist you in person, showing you how the trick works and what you need to do to successfully complete it.