>Chinese romanization is a pretty weird business, I'll grant you

It's far more consistent than English's use of the alphabet, honestly.

> - who
>would know from looking at "Dìqiú" that it's pronounced
>"DEEcho"?

Dee-chyo, actually. The -iu is a contraction of -iou, which is pronounced "yo" (basically); since there's no syllable that sounds like "yu" in Mandarin, and hanyu pinyin is big on the economy of letters, the "o" is omitted. (Similar to how "-ui" is pronounced like English "way" -- it's basically "uei" with the "e" omitted.)

Essentially, you can get by knowing these:

Consonants: Q and ch are both "ch" sounds (they're actually not the same sound, but they're very hard to distinguish for most monolingual English speakers), and x and sh are both "sh" sounds. J is a hard "j" like in "just," never a "zh" sound (that's spelled "zh"). G is always a hard "g", like in "girl," never the "j" sound. C is "ts" sound, like the "ts" at the end of "cats"; z is the same sound, but voiced (like, say, "ds" at the end of "lads"), but in this context it's fine to leave it unvoiced. The rest are close enough to English consonants you'll be okay going that way.

Vowels: i is usually "ee" by itself, but when it's the sole letter following the consonants z-, c-, s-, zh-, ch-, sh- or r- in a syllable, it's more like an "er" sound. When i is followed by other vowels in a syllable, it becomes a consonantal "y," essentially.

a is basically English father. This is always true; -ang always like "song" (give or take), never "sang" (past tense of "sing").

e is an "uh" (schwa) sound in most contexts.

o is never by itself; if the long "o" is a syllable's vowel sound, it's written as "ou".

u by itself is an "oo" sound, like English "rude", and never ever implies the "y" sound in, say, English "cute" (that's i's job). If "u" is followed by another vowel, it becomes a "w."

ü is kinda tricky for English speakers, since it's not used in most English dialects; it's like an "ee" sound but with lips rounded.

For most vowel digraphs, if you know Japanese romaji orthography, you'll be able to get close enough to not drive people who've studied Chinese batty. The two gotchas I mentioned upthread: "-iu" ("yo") and "ui" ("-way").

Lastly, diacritics: the macron (overbar), acute accent (ˊ), caron (ˇ), and grave accent (`) mark tone: flat tone, rising tone, falling-rising tone, and falling tone, respectively. These are really really important; tones affect lexical meaning (the only difference, in pronunciation, between "horse" and "mother" is tone), not just semantics as in English. The fifth tone (neutral) has no diacritic.

Wikipedia article on pinyin for more info.

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