This is just going to be a relatively brief overview with some things to watch for as well as some resource links. I was going to write a thorough guide, but I was over looking at the Wikibooks pronunciation article and it's actually really great if you want an in-depth description.
Japanese pronunciation is relatively easy for an English speaker. Probably easier for someone who knows Spanish or Italian, but it's not too bad. There is 5 vowels and 14 consonents, and they're all pronounced consistently. The vowels are more or less the same as in Spanish/Italian, and the majority of consonents can be approximated pretty easily from the romanizations.
The consonants are generally paired with vowels, with some exceptions. N(m) and all of the vowels can fly solo.
This would be a good time to mention that I highly DISRECOMMEND using only romanization to understand how to pronounce things in Japanese.
The whole system makes more sense if you become proficient in reading Kana. a standalone "n" is actually a different sound than an "n" paired with a vowel (na,ni,nu,ne,no). When standing alone, N/M(ん) in japanese is a NOT like an N generally is in English; instead it sort of sounds like humming. If you take your tongue and act like you're going to say "gnat" or something and just hold the "n" sound and hum, that's sort of what you're going for.
If you pair it with a vowel, such as in No(の), then the pronunciation is pretty close. The difference between En and Jp no/の is that the "n" sound is kind of short and sweet in Jp.
In fact, if you carefully listen to a native Japanese person speaking you may be able to notice that when they use consonents they sort of micro-stop on the consonants. I think that English speakers tend to kind of muddy their speech with the consonants whereas in JP the consonants seem to be sort of short and quick in their pronunciation.
Even with a double consonant (such as in kitte/きって) the pronunciation is still short and quick, it just has a pause before you actually say the "t" sound. The exception being with that trixy ん sound from before, like in ko(n)nichiwa. There you actually end up holding the N sound using that humming nasal pronunciation as above.
Speaking of double consonants, I'd like to talk about something called haku (拍) or mōra (モーラ). So, Mora(e) are like beats in music and use the same kanji (拍) as beats in music (ie. 1/2/3/4 in 4/4 time).
Basically every consonant pair, vowel, and ん take up one "beat". So if you were to set a metronome to someone speaking in rhythm with that metronome, each syllable would fill the same amount of space.
So, for example, Arigatou is A/ri/ga/to/u -- 5 beats; Konnichiwa is Ko/n/ni/chi/wa -- again, 5 beats.
It's actually pretty important, because if your timing is off you could end up saying a different word. For example: ki/te (2 beats) and ki/t/te (3 beats). Also, since I mentioned Arigatō:
R -- Beware the R
If you can do a Spanish R, it's pretty much the same except for kind of vanilla with there being no trills or anything funky... If not, it's sort of this sound that's in the middle of "r"&"l" with a little bit of "d" sprinkled in. Stay away from those soft rubbery arrrrr sounds. If I'm saying RO in Jp, it's more like if you're saying doe with your tongue in the shape it would be if you said low than having your tongue on the bottom of your mouth when you say row... If that is actually intelligible to anyone other than myself.
Another minor point is that sometimes they kind of skip their vowels. Not a big deal if you say them with the vowels, but a native speaker will probably skip them if speaking quickly. It's also pretty common at the end of words to kind of half-say the vowel. Examples: su/ki becomes s'ki, ki/ke/n becomes k'ken, and the ubiquotous de/su becomes des'. They tend to still mouth the vowel - it just doesn't get fully voiced.
Last thing to watch out for is pitch accent & intonation in Japanese. Now, if you were to try and memorize all of the different accents in Japanese and how they affect meaning you'd probably just end up giving yourself a splitting headache. Good news is that it's not anything worth stressing over or going out of your way for. I take this point from Niko's Course (mentioned in my LJ#1 post), not being highly proficient in Japanese myself, but apparently context is far more important. So just be aware that there is a pitch accent and try to emulate native Jp pronunciation.
(How the heck do I pronounce this crap??)
Overall, when actually trying to pronounce Japanese (or really any language you're learning) you kind of want to be hypercritical of your pronunciation so that you can avoid falling into bad habits. And be open to changing the way you pronounce things if you find that you're not doing it right.
Pretty much everyone universally knows Konnichi(wa) (こんにちは) and Arigatou (ありがとう), but most of the time when I hear English natives say them they murder the pronunciation. I hear a lot of konitchywa and arrihgato... Not that I pronounce everything perfectly, but I pay attention to the way that I pronounce things for that reason.
You just have to put in a lot of care and effort into learning the pronunciation is all. Learning a language is work. If you put in half-assed effort you're going to get half-assed results.
Bad joke, but my mom always told me that if I was going to do something I should use my whole ass insead of half assing things.
So, now you know how to listen to Japanese for pronunciation. If you want a detailed guide on the pronunciation of syllables, I recommend checking out the article and videos below.
Thanks for reading! Have a Super Rad kind of day.
Side note: You might be wondering what those squiggly things are above in parenthesis. Those are Kana; specifically Hiragana. They will be discussed more at a later date, but they're really not all that scary. It took me a day or so to learn them all and I pretty much just review them to keep em fresh.
PS. If you want more detailed information on this stuff, check out this pronunciation article... they really did a good job on it...
Wikibooks Japanese Pronunciation: Click Me!!
PS: I would be interested in a footer for my posts, if anyone would like to design one for me... I'd be willing to toss some SBD over for it.