The Chinese writing system is NOT alphabetic, but is instead based on characters. Each character is composed of a number of basic strokes which must be written in the correct order
So, the Chinese alphabet? There isn't one - if you mean a set of basic Chinese symbols that are used to spell words. But there is Hanyu Pinyin - the official romanization system. Most people who learn Chinese start by learning pronunciation - these days Hanyu Pinyin (or just Pinyin) is the most commonly used tool.
There are no direct clues as to how each character should be pronounced. Learning to read and write Chinese can therefore be quite a lengthy process, since a knowledge of several thousand characters is needed to read a newspaper.
It really depends on your goals. Why are you learning Chinese in the first place?
Most language courses start by teaching Simplified Characters. For practical, everyday purposes this is the most useful. But to go beyond a superficial understanding of Chinese culture, learning both the traditional system used in Hong Kong, Taiwan and most overseas Chinese communities, as well as the simplified one now officially used in China, is a good idea. The latter came into being after the 1949 Communist Revolution and was promoted as a way of increasing literacy among the uneducated masses. The two systems do overlap considerably - so anyone who has learned traditional characters should not have too many problems learning simplified characters (and vice versa).
China is written 中國 or 中国. The first is in traditional characters, and the second simplified.
A common misconception about Chinese characters is that they are based on pictures of the objects or ideas they represent. Only a small number of characters are descended from pictures (such as the characters for sun, moon, tree, etc).
And, not surprisingly, the concrete origins of the modern versions of these so-called pictographs are usually difficult to detect.
If nobody had told you that 月 was originally a picture of the moon, you probably wouldn't have guessed! And does 日 look like the sun to you? Even if 木 could pass for a tree, the modern meanings in Mandarin Chinese have changed (when we talk about these characters as radicals we gloss them as "sun", "moon", and "tree", though).
These days, 月 by itself usually means month, 日 is day (or -th when writing the date formally), and 木 is found in compound words related to wood.
So, unless you're writing classical poetry, you'll need to use two characters for moon: 月亮, and a completely different compound 太陽 for sun. For tree, 樹 is used.
Some learners find that breaking characters up into their various components is helpful. It's a good idea to familiarize yourself with the basic strokes and stroke order first.
Next, you'll be ready to learn how to analyze characters into their components. Most characters are based on the principle of radical + phonetic.
The radical, or semantic component, is often found on the left hand side. It gives a rough indication of the meaning.
The phonetic, or sound component, gives a pronunciation clue.
Look at 馬 ("horse") and 嗎 (a question marker) - 马 and 吗 in their simplified forms - and you'll see an illustration of this principle. Note that they have common components. The character on the left serves as a sound indicator in the one on the right. 嗎 has the "mouth" radical 口 . Both 馬 and 嗎 are pronounced ma - although with different tones. So, the meaning of 嗎 has nothing to do with "horse" - it just borrows 馬 to give a sound clue.
But that's an easy example!
As this practice has been around for at least two thousand years and many characters have changed their pronunciation and meaning quite drastically, a knowledge of radicals and phonetics can rarely serve as anything but a rough guide.
Still, it is often helpful to the learner to know that there is a system at work - however imperfect - in the composition of the characters.
Learning to recognize around 50 of the most common radicals out of the total 214, will certainly be a good start. On the other hand, you can certainly learn to write something simple - like the months of the year - just by combining the numbers (1-12) with 月
Another misunderstanding about Chinese characters is that they represent words. Since a character is generally equivalent to a syllable, it is widely held that Chinese is a monosyllabic language.
That is, that each syllable in Chinese is a separate word. Although each character has a meaning, this is not the same as saying each character is a word.
It is more accurate to say that each character is a morpheme. A morpheme is a linguistic term to refer to the smallest meaningful unit in a language.
For example, in English, we can say that -s, is a morpheme, since it carries the meaning of plural. More examples can be found in the various suffixes originating from Latin and Greek, e.g. -ion, -ize, pro-, in-, re-, etc.
Imagine what English would be like if it had never been influenced by outside languages like Latin and Greek. We would have to use a combination of native English words to express these ideas.
So, although in classical written Chinese, characters are very often equivalent to words, in the modern, colloquial language, there is a greater tendency for words to be polysyllabic.