There are four parts to learning to read any foreign language: the symbols, their meaning, grammar, and pronunciation. The most basic thing is to learn to recognize the symbols that belong to the language. Where does one symbol end and the next begin (consider: cursive writing) and what do the symbols mean (consider: hierglyphic writing). The grammar of the language provides the rules for linking symbols together to form words, phrases and sentences. Finally, the sounds associated with the written symbols, if any (consider sign language), can be important in deciphering some meanings or their historical origins.
The Chinese writing system is concept or idea based rather than sound based. English uses just 26 letters to represent a sound/meaning combination (consider: too, to, two). Many words in English can be broken down into roots - syllable or sound clusters that have their own meaning. For example, the word telephone can be broken down to its Greek roots tel meaning far and phon meaning sound. Now imagine assigning a distinct symbol to each of those meanings say: ⇜ means far, and ☊ means sound. In that case the word for telephone might be ⇜☊. Time passes and telephones are everywhere and we want a shorter way to represent that concept so we overlay the ⇜ symbol on top of the ☊ symbol and get a new symbol ☎.
That is how many Chinese characters evolved. The majority of the characters you encounter in Chinese texts represent a specific concept and create more complex ideas by building compound words with 2, 3 or 4 character combinations. See this excellent decomposition of the two characters that make up the Chinese word for computer.