Okay, for all of you who want to act like you know Spanish, but have butchered all attempts to read out of a phrasebook you found, say, here, here's how to pronounce it generally.

First off, let's start with the vowels:

a is pronounced as in father and Mafia;
e is kind of between fetch and day; just think a pure "eh," but it is not "ay";
i is pronounced like people, weed, and beast;
o is like home, but rounder; again, think of a purer version of "oh";
and u is like boobs and peruse.
y is pronounced pretty much like the American "y," except when it's by itself, in which case it's pronounced "ee." However, in some South American countries, it's pronounced like leisure, a sort of "zh" sound.

Now for the diphthongs. In case you don't know what that is, it's the sound you get when you combine two or more vowels together. Really, when you think about it, the diphthongs define themselves, given the sounds of the constituent vowels. But anyway...

ai is pronounced as in right, pie;
ei is pronounced as in weigh (wow, look at all those silent letters in English *tsk*) and pay;
oi is pronounced like ska bands do it: "oy!" More generally, it's pronounced like boy and moist.
au is pronounced like rout and mouse;
and eu, as my dictionary best puts it, is "like the vowel sounds in English may-you, without the sound of the 'y.'"

Whenever u is the first vowel in a diphthong, it sounds more or less like the English w.

Yay, we're up to consonants!

For the most part, the consonants in Spanish are pronounced like their American equivalents, so I'll outline the exceptions here.
b is like our b, but a bit softer; the lips do not really come together all the way. This is the reason that the capital of Cuba, spelled "Habana" in Spanish, is spelled "Havana" on our maps.
c is pronounced like an English k if it comes before a, o, u, or a consonant; it is pronounced like an English s if it comes before e or i.
ch is pronounced like the English ch in "chips" and "channel."
g is a hard g, as in "girl," when it's before a, o, u, or a consonant. Note that if the g is followed by a u and an e or i after that, the u is silent, unless it has a dieresis above it (ü), where the u is pronounced like an English w. (Compare "guerra" (geh-rra) and "antigüedad" (ahn-tee-gweh-dahd), but also "guapo" (gwah-po).) If it's followed by e or i, it's pronounced just like the Spanish j.
h is always silent. Period. "Hoy" is pronounced just as if it were "oy." So don't pronounce the h!
j is pronounced like Bach or loch, but it has no real English equivalent. Think of an English h, then think of hocking up a loogie, and cross the two. That's about it.
ll (that's two L's) is pronounced like the Spanish y, only with a bit of a preceding l. See above.
ñ: just think of the Three Stooges saying "nyuk, nyuk"; that would be spelled in Spanish "ñak ñak," more or less. If that doesn't work, surely you've heard the correct pronunciation of piñata...
q always sounds like an English k, and is always followed by a u, which is always silent.
r is a strange beast to us Americans; it is a small flick of the tongue to the roof of the mouth, called in linguistic circles a "flapped r." Now say the word "better" for me really quick. If you said it like most Americans do, you made a flapped r right there in the middle of the word. This r is used for all r's in Spanish, save for the case of...
rr, which is pronounced like the people doing the "drumroll" at the house-lighting in National Lampoon's Christmas Vacation. Just "trill the tongue"; there's really not a better way to describe it (none that I can think of, anyway).
w, found in only a few foreign words, is pronounced like an English v;
x is like the gs in "big sack," sort of a softer version of our x. Before a consonant, it's the same as a Spanish s.
z is like the English s, not like the English z.

Now, for the final piece of the pie: Accentuation.

In order to properly accent a word, you have to divide it up into syllables. It goes something like this: i and u are weak; everyone else (a, e, and o) is strong. This means that if you have a combination of two strong vowels, they are pronounced as separate syllables (as in pa|e|lla, tra|er). If you have a combination of a strong vowel and a weak vowel, they are combined, the strong vowel is the main one pronounced, and they are said in one syllable (as in sen-ti-mien-to, cin-cuen-ta). If you have two weak vowels, they are combined into one syllable and the second vowel is the main one pronounced (cui-da-do, viu-da).

So, now that you've got the syllables properly separated, remember this: The second syllable from the end is the accented one if the word ends in n, s, or a vowel (not counting y). Otherwise, the accent falls on the last syllable. So, given that, let's accent some words: hacer, hago, and edad, just to name a few.

Now, if you should see an accent mark in the word, you can just toss all those rules out the window and accent the syllable that the accent mark falls on. The accent of a word can change the meaning, so be careful! (Example: "esta" (ehs-tah) means "this," while "está" (ehs-tah) means "it is.")

Before I wrap this up, I suppose I should mention one other thing: native speakers tend to combine vowels between words. For instance, the phrase "primero y último" wouldn't be sounded out word by word, but would rather be said something like "pree-mehr-oh-yule-tee-moh." Do that for your first year Spanish class and earn bonus points. :)

Well, that's about all you can know about pronunciation from just looking at the words. Msg me if you have anything to add, and I know I've done at least something wrong here. Thanks in advance for your input.

Gritchka points out to me that I should note that this Spanish specifically refers to the Central and South American variety; the Spanish (Castillian) kind has some fundamental differences—most notably, the pronunciation of z and c, when they would normally be pronounced like s, like the English th.