These are characters which are based off of the actual image of an object. Naturally these were the first, most early developed symbols to describe common everyday things. e.g. 月 木 日 .
These are diagrams of concepts that either do not have form or are difficult to describe by a simple picture. The most common example of this are the characters 上 and 下.
Ideogrammic compounds 會意字
This type of character is essentially the combination of two or more pictograms and/or ideograms. The classic example is when you combine two trees (木) you get a forest (林).
Phono-semantic compounds 形聲字
These characters have two parts, one part is a pictograph which stands for the approximate meaning, and the other is another character which stands for the approximate sound. A common example is 河 river, 湖 lake, 流 stream, 沖 riptide (or flush), 滑 slippery. Notice how these examples all share the water radical and all refer to some type of water body. The remaining part of the character signifies the pronunciation.
Derived meanings 轉注字
These characters maintain a distinct meaning at the same time they also posess an abstract meaning. e.g. the character 交 originally mewas a pictograph of a man sitting with crossed legs. This can be interepreted loosly to mean exchange or communication.
Arbitrary Meanings 假借字
These are characters that originally meant something else but later came to mean something completely different. One example is the character 來 which is a pictograph that means grain. However, out of necessity, it became used for the word to come.