The system of Chinese Alphabet symbols used in Taiwan is called Zhuyin.
Foreigners often refer to these letters as Bopomofo because of the sounds of the first four "letters' or symbols.
The letters in this Chinese alphabet are phonetic. Used to spell out Mandarin Chinese, a single Chinese Symbol's pronounciation will use between 1 and 3 "letters" and will also include a tone mark, for five different tones. (In general the five tones are indicated as follows: ¯ˊˇˋ˙. But, in zhuyin the first tone symbol is not used.)
Note, when written with Chinese characters, these letters are written vertically from top to bottom, generally to the right of the character, with the tone mark to the right of the letters. You may find it written from left to right in some texts particularly when written with the Chinese symbol whose sound they represent.
One thing that can be tricky when pronouncing Chinese symbols, is that the sound of the characters consenants and vowels can affect the way the tone sounds, at least to foreign not-yet-used-to-mandarin-Chinese ears.
And so you have to learn to listen carefully to the sound of the character to sense the difference between the sound of the vowel component and the sound of the tone.
It's tricky and one way that I've gotten used to it is to use the gwoyeuh romatzhy romanization system as a pronounciation guide. It's requires a lot of work to memorize but used in conjunction with either the Chinese alphabet or pinyin (the more common way of writing the sound of Chinese characters) it can help.
And so in my own guides and resources I often include GR spellings as a pronounciation guide. Even just reading through the GR spellings you can learn to see how certain vowel sounds naturally cause a rise or fall or dip in tone. And the GR spellings take advantage of this. Rather than using tone marks the GR system uses spelling so that tones come out naturally due to the spelling of the word.
In total the Chinese alphabet has 39 letters or symbols.
Without tones these can be combined to create a finite number of sounds with between one and three symbols.
Lets look at the symbols individually first and then look at some of the possible combinations.
The first group of alphabetical symbols are:
In pinyin these can be written as
B, P, M, F
The B and P are both soft (bih or pih) with the main difference being that the p is said with a puff of air and the b without.
The M and F are also soft sounds (mih, fih) and again the F is said with a puff of air between the lips (aspirated) and the M without said puff (unaspirated)
The unaspirated M and F sounds can feel like they are reverberating within the cavern of the mouth. The P and F sounds can feel like you are blowing or spitting them out (much like saying the F-word in English as opposed to saying a-hole under ones breath.)
The next set of Chinese alphabetical symbols is :
In pinyin these can be written as: D, T, N, L.
The D and T sounds are both soft (Dih and Tih).
Likewise the N and L sounds (Nih, Lih).
This group of symbols follows a similar pronounciation pattern to the first group. The first and third letters are not blown while the second is. The fourth one is done with the tongue flicking forwards as you say it (but kind of don't spray it.)
(Note, using the ih ending here is a bit tricky. I could have used a uh or even an eh ending instead but hopefully what you'll find is that as you learn more of the pronouncation, the ih ending is more consistant with what follows.)
The above Chinese phonetic symbols are all consanants.
Let's look at some vowels so that we can combine the consonants and actually make meaningful sounds (or at least, sounds that have the potential to have meaning. The first three vowels are:
These Chinese alphabet symbols can be pronounced as: yi, wu, yu
The yi sound can be made with wide lips, like a fake smile. It sounds like a long e sound. The wu sound is made with rounded lips, like puckering up for a fake kiss. This sound reverberates more in the cavern of the mouth. The yu sound, which sounds like ew (that's gross) or "you" (as in "hey you") but is more nasal, up in the nose. You may find that your ears pull up when you try to say it.
This sound latter sound is not used by itself. Yi and wu on the other hand are.
Here are some combinations with the GR spellings for all four tones plus, in brackets, the basic pinyin, a roughly equivalent English pronouncation guide and whether to blow or not blow.)
Here are the combinations without the GR (so you can practice).
The next set of vowels is
These can be pronounced as: ah (soft), oh (soft), between ih and uh (soft) a long eh (soft)
Personally I think the vowels can be some of the hardest elements to say and differentiate. And that's why I'd suggest practicing them them early on. So that you can practice differentiating their sounds.
With the Chinese letters used so far, the only combination that uses the ㄝ letter is another vowel
This can be pronounced a little like yeah as in a "hell yeah". Here's its GR (and pinyin)
Here they are combined with the first 8 consanants with their GR (and pinyin) pronouncations)
I've shown theoretically possible combinations which also includes sounds that aren't actually used. It may be helpful to be at least roughly familiar with the sounds that aren't used.
Take out the frustration of looking up Chinese characters, even if you are a beginner.
The Easy Lookup Chinese English Dictionary makes Simplified and Traditional Chinese character lookup, easy even if you don't know a characters pronounciation.
Find out more about the Easy Lookup Chinese English Dictionary