In English, we have a number of words that are spelled the same way but sound different and have different meanings. These are called heteronyms. They shouldn't be confused with homographs which are words that are spelled the same but have different meanings, and homophones that are words that sound alike, have different meanings, and different spellings.
A common example of a heteronym is the word lead. I can lead someone to pick up a piece of lead.
An more interesting example is the word August. As a proper noun, it's the month and has emphasis on the first syllable when pronounced. As an adjective, it's describing someone and has emphasis on the second syllable when pronounced. August is also an example of a capitonym, or a word that has a different meaning when it is capitalized.
Now, you could argue that these types of words would be more common in English, given we only have 26 characters to play with when creating words. And if Chinese has tens of thousands of characters, does it run into the same problems?
And the answer is yes.
A simple example is this character: 还
I can use it like this:
我还没有那本书。（Wǒ hái méiyǒu nà běn shū）
In this case, the word is 还 (hái) and means "still". The sentence above means "I still don't have that book".
But exactly the same character can be: 还 (huán). It means close to the English equivalent of "return" as in returning something to someone.
Here are some other common examples:
银行 (Yínháng) – this is the word for a bank. The second character is háng. But the same character can be Xíng with a lot of different meanings.
长 is chang or zhang
了 is le or liao
着 is zhe or zhao
And so on. So you might start to understand the real challenge of automatic translation by computers. If you just type 长 how would the computer have any idea what you meant? The answer is that you have to give it context (i.e. more to go on) before it can decide that.
I'll write more soon on the best methods for learning. If you want to get a taste for it in the meantime though, my current favorite site is iTalki, and my favorite teacher by far is Amy He. If you decide to try it, click here and it's cheaper for both you and me.