The problem with the Hanyu Pinyin system is that often, the words still do not give the proper pronunciation, but rather assign certain Roman letters and combinations of letters to certain Mandarin sounds. This is because many of these sounds or distinctions between sounds do not exist in English or almost any other European language.
The sad fact is that Mandarin can never be properly rendered in regular Roman script, because we simply do not have enough letters to go around, and many of the sounds or so completely foreign that it is difficult to even make an approximation.
So, the best way to show an English or SAE(Standard Average European) speaker how to pronounce Mandarin sounds from the Pinyin is to describe the sounds, as would the International Phonetic Alphabet, many of whose symbols are difficult to represent here, but can be found at http://www.arts.gla.ac.uk/IPA/fullchart.html . The IPA is the more or less standard alphabet used by linguists to represent phonetic sounds, which almost any language's orthography pretty much always sucks at doing(English is notorious for this).
Anyway, here are the sounds (generally), in Pinyin, the ever-popular and outdated Wade-Giles system, and IPA or a phonetic description (IPA listings with an asterix are not the true symbol, but the best I could do with the character set I have):
INITIAL SOUNDS:
-- b p /b/, but with very little or no voicing, which should be easy for English speakers, since we do not voice stops very fully at all. It could actually be more similar to 'p' in any SAE language like Spanish.
-- p p' /p/, like the English word 'pop,' with a heavy puff of air following the stop. This is called 'aspiration'Again, this is no problem for English speakers, since we do it anyway.
-- m m /m/
-- f f /f/
-- d t /d/, with the same rule as for 'b'
-- t t' /t/, with the same rule as 'p'
-- n n /n/
-- l l /l/
-- g k /g/, with the same rule as for 'b' and 'd'
-- k k' /k/, with the same rule as for 'p' and 't'
-- h h /x/, this sound is a voiceless velar fricative, like the Greek 'chi,' or like the sound in the German 'machen.' This is pronounced in exactly the same place as 'k,' but instead of the air stopping, it is blown through with much friction. This same relationship exists between 't' and 's.'
-- j ch(i) /dzh/* This sound is a lot like the 'j' in English, but more palatalized. The English 'j' is actually a combination of two sounds, /d/ and /zh/, a sound like the 's' in 'measure.' This is slightly more palatal sounding in Mandarin, as if you said 'jyeep.'
-- q ch'(i) /tsh/* Like the 'ch' in 'chase,' but more palatized, like 'chyase.' This is also aspirated, like 't' 'p' and 'k,' but this is done anyway in English.
-- x hs,s /sh/*, but more palatized, like
saying 'shyeep'
-- zh ch /dzhr/* a lot like the 'j' in English, but retroflexed. Retroflection is done by curling back the tip of the tongue(Retroflection is very common in Hindi, and is often heard in stereotypes of Indian people).
-- ch ch' /tshr/* like the English, 'ch,' but retroflexed.
-- r j /zhr/* like the sound in measure, but retroflexed.
-- z ts,tz /dz/
-- c ts',tz' /ts/
-- s s,ss,sz /s/
MEDIALS AND ONGLIDES:
-- i i /j/ the 'y' sound in English 'yet'
-- u u /w/
-- y(u)/(l/n)ü ü /y/ This sound is a lot like the 'u' in the French 'lune' or the 'ü' in the German 'über.' It's a very easy sound to make, just say, 'tea,' but round your lips as if the sound was /u/ and not /i/.
-- y y /j/
-- w w /w/
-- y(u) y(ü) /y/
FINAL SOUNDS:
-- a a /a/ like 'a' in 'father,' but a little more fronted before /n/.
-- o o /o/, but when it follows a consonant, it's /wo/. Mandarin 'po' is pronounced /pwo/
-- e e,ê,o,eh /uh/*, /eh/* This sound is a lot like the 'uh' sound in 'cut,' but a lot tenser sounding. When it follows one of the medials or onglides, it is pronounced like the 'e' in 'bet.'
-- ai ai /aj/ like in 'buy' or 'high'
-- ei ei /ej/ like in 'pay' or 'weigh'
-- ao ao /aw/ like in 'how' or 'cow'
-- ou ou /ow/ like in 'mow' or 'foe'
-- ian ien /yehn/* just like the Japanese 'yen'
-- ng ng /ng/* Like in 'sing'
-- er er,erh /er/ Like in 'herd'
-- i i,u,ih /i/,/ih/*,/irh/* This is a bit complicated. Normally, it is /i/, but following (pinyin) c/z/s, it is pronounced like the 'i' in 'bit.'And after sh/ch/zh/r, it's like 'bit,' but the vowel is retroflexed.
-- u u /u/ like 'food' or 'dude.'
-- (y)u,(l/n)ü ü /y/
-- un un /wuhn/* like 'fun' but 'fwun'
-- o(ng) u(ng) /oo/* like in 'look' or 'wood.'
Of course, tone is always important in Chinese. Mandarin has five tones. There are a few ways to represent this. One is to use the number 1, 2, 3, 4, or 5 following the word. This often results in a very hard-to-read transliteration. The one I like uses a series of diacritics over the vowels. Here are the tones:
1. High and long 'ā'
2. Rising and long 'á'
3. Low(Dipping) and short 'ǎ'
4. Falling and short 'à'
5. Neutral 'a'