Decide if you would like to learn the simplified or traditional versions of the characters. The traditional characters have more strokes and radicals and can be more difficult to memorize and write, but are easier to recognize and read than the simplified versions. The simplified characters are from the 20th century and are used in Mainland China and Singapore, while in places like Hong Kong, Malaysia, Taiwan, and Chinese communities outside China, the traditional form is favored. The traditional tends to be more popular, as it's more versatile and is the form used in calligraphy. Only about 2,000 characters have simplified versions.
Learn a few characters, perhaps your name and a simple sentence, and then familiarize yourself with the "radicals." Radicals are the parts of the character that come together to make up the whole. Some represent sounds, and some represent meaning, making it difficult to guess what a new character means, but easy to see the logic once you know the meaning. Recognizing these elements and how to write them will greatly aid in learning new characters as you build your vocabulary.
Pay attention to stroke order. As you learn to write, you must execute the strokes of the character in a specific order, and starting from a specific direction. The character is considered incorrect if you don't follow this rule, even if the finished product looks identical to one completed with the proper stroke order.Many learning materials for beginners will mark numbers next to the strokes to indicate their order.
Write every day. Because characters are easily forgotten, it's important to keep even the basic ones that you first learned fresh in your mind, or you'll have to relearn them. Integrate new ones into sentences using ones you already know. Chinese grammar is relatively simple, so you can become quite proficient in writing simple sentences if you invest the time and patience into consistently reviewing old characters as you memorize new ones.