Michael Hackett, don't know if this will help you or not...
In Japanese, all the vowels are pronounced thusly:
A as in aww (rhymes with law)
I as in ee (rhymes with key)
U as in ooh (rhymes with you)
E as in ay (rhymes with day)
O as in oh (rhymes with toe)
So the full list is:
k s t n h m y r w
a ka/ga sa/za ta/da na ha/ba/pa ma ya ra wa n
i ki/gi shi/ji chi ni hi/bi/pi mi ri
u ku/gu su/zu tsu nu hu/bu/pu mu yu ru
e ke/ge se/ze te/de ne he/be/pe me re
o ko/go so/zo to/do no ho/bo/po mo yo ro wo
The nice thing is that the sounds are pretty much universal as there are few exceptions (though my experience with Japanese is limited to one year in college, so I could be wrong here). The other quick guide line is that everytime you see a vowel, that's one syllable. So for example, keikogi it is pronounced kay-e-ko-gee (gee rhymes with see). The kay-e part kind of runs together very fast though.
If you see the letter 'n' (or 'm' sometimes) , then technically it is it's own syllable, but really it gets included in the syllable of the vowel just before it. For example, senpai is pronounced sen-pah-ee (but the last two syllables are spoken so fast, it sounds like one syllable...this is generally though not always true whenever you see two vowels together, so really it sounds more like sen-pie). Another example is sandan (sahn-dahn). There's a catch though, and unfortunately you need to see the kana or kanji to really know how to pronounce it, since there is an 'n' sound all by itself, and also the phonetic sounds, na (nah), ni (knee), nu (new), ne (nay), no. The rule of thumb here is that if you see a vowel, followed by 'n' which is then followed by a consonant, then the 'n' sound gets attached to the vowel preceding it.
Another key to help in pronouncing Japanese words are understanding how Ya, Yu, and Yo work. If you see a word with a consonant followed by a 'y', for example in Nikyo, then it is composed of the phonetic sounds, Ni-Ki-Yo, but instead of being 3 syllables, it's actually only two. The Ki and Yo get merged into one syllable kyo. The same holds true with ya and yo if the letter preceding the 'y' is another consonant. Related to this, if you see, 'sha', 'shu', or 'sho', it is really the sounds: shi+ ya or chi+ya (sha/cha), shi+yo (sho) and shi+yu (shu) so for example, yudansha is pronounced you-dahn-sha.
The last trick are double consonants as in Ikkyo. It's hard to explain this one, but it's a guttural stop, where you sort of start saying the consonant, and abruptly stop it, then say it again. So it goes something like, eek-kyo. At the end of the first syllable with the double consonant, your tongue should be at the roof of your mouth. The other hard to explain part is that this is technically 3 syllables, but when I hear Japanese say it, it sounds like 2 syllables to me. As another example, bokken would be pronounced, bowk(rhymes with oak)-ken, but again, even though technically this word is 4 syllables long (bo-k-ke-n) if you hear it spoken, it is really only sort of 2.
Two last examples. If the vowels i or u comes inbetween the consonants, k, s, h, t, or p, then the vowel is silent. For example in bokuto, it's pronounced, bow-k-toe (the k is like when you are about say could, but leave off the 'ould' part). Notice it's still 3 syllables, it's not pronounced like bowk-toe. The final example is that most of the time (but not always) if you see 'o' and 'u' together, it's pronounced as one long oo (rhymes with row) sound. For example, sometimes arigato is romanized as arigatou. This is because arigato is actually a-ri-ga-to-o (it is 5 syllables long, so the o sound at the end is extended one extra beat).