Chinese is based on “Symbols”, in Chinese we say "象形"(xiàngxíng). Our ancestors had created these beautiful characters more than a thousand years back, and we still use them until now; most of the Chinese characters could be explained and recognized by each characters' STRUCTURE, like 部首radical(bùshǒu); and be understood by 形聲(xíngshēng: radical plus phonetic to form a character; to use the same root for getting a similar pronunciation) and 會意(huìyì: understanding or knowing; to combine some related words to present a new meaning). Therefore, they indeed have some kind of interconnections.
As you can see, most of the famous Sinologists(David Hawkes,Cecilia Lindqvist...) study Chinese or even Chinese society, all start from 漢字(Hànzì), they learned from traditional Chinese then traced back to ancient Chinese, because from the Structure of 漢字, people can extract the logical meaning of a Chinese character and easily recognize it; furthermore, to understand the Thoughts, Culture or even the World of the Chinese. That's the true essence of "從漢字習中文"(zòng Hànzì xí Zhōngwén).
When you get some clues about the logics from the Structure of a 漢字 you will get more fun from learning. In case you have learned simplified Chinese, you still can have a lot of fun in re-learning them the traditional way.
There are some professional methods to recognize 漢字, but I only choose a part of them as the major tips to the beginners and will introduce them gradually. If you can follow the first two rules below, you can get some hints of a character easily, like pronunciation or category; if you use the third rule flexibly, you can get a lot of fun while learning.
1. 部首: You can classify the category from the RADICALS 部首.
Example:
With the radical 雨 (yǔ:rain) you can guess the meaning of 霜、霧、雪…
They are all related to 雨, even though you don’t know these words yet.
2. 形聲: You can guess a similar or the same pronunciation from the ROOT 字根(zìgēn).
Example:
With the root 平(píng: fair; flat) you can surmise the pronunciation of 評、坪、萍…
They have the same or a similar pronunciation.
3. 會意: You can interpret it from it’s COMBINATION 組成(zǔchéng).
Example:
看(kān: to see or to look)：consists of 手(shǒu:hand)+目(mù:eye). When people want to see something clearly, they might put their hand above the eyes, to block the sunshine, so 看 symbolizes "to see" or "to look".
Let's just take an example you might already be familiar with, to see if you get any new feeling after the interpretation below.
“ 您好”(nín hǎo)！ Many people know 您 is much more respectful than 你; 好 means good… But why is 您 much more respectful than 你? And why does 好 mean good? Kindly follow me to note their COMBINATION.
You can find that there are two words inside 您：
The upper side is 你(you)，
The lower side is 心 (heart);
In case someone puts you in his mind, it symbolizes you are very important, that’s why 您 is the respectful form of 你。
Let’s move to 好. As you can see 好 also consists of with two words：
On the left-hand side is 女(nǚ；female), on the right-hand side is 子(zǐ；child).
If a man gets both a wife and a child, it means that everything almost has been settled down and he can be very lucky. So his "good" situation is symbolized by "好"。
As long as following this method, you got the actual meaning of word but also learned much more vocabularies inside: six words totally, 您，你，心，好，女，子.
