Spanish pronunciation is fairly easy for an English speaker--Spanish contains only five vowels, while most English dialects have around 15. The sounds that typically give English speakers trouble are the trilled "r" and the "b/v" sound. I warn my dear readers that despite extensive study and experience with the Spanish language in many countries, I am not a linguist, and my suggestions may not be considered Linguistically Kosher. This is intended to be a practical guide for the casual user, so I am not going to delve into complicated phonological terms, mostly because I don't understand them. However, I can almost guarantee that if you follow these rules, no one will look at you funny. Unless you're wearing a Hawaiian shirt. Then you pretty much deserve whatever you get.
Vowels:
a: Pronounced like the English "ah", as in "father".
e: Pronounced like the short "e", "eh", as in "enter".
i: Pronounced like the long "e", "ee", as in "between".
o: Pronounced like the long "o", "oh", as in "dope".
u: Pronounced like the long "u", "ooh", as in "woo".
Consonants:
b: "b", known as "b grande", or "large "B", in some countries, is pronounced the same as "v", "b chica". "B" is generally pronounced the same as the English "b" before a vowel (bag), although it tends to run into the "v" sound, making the result like a mix between "b" and "v". Pronunciation differs greatly by region.
c: Before "a", "o", "u", or a consonant, pronounced like a "k", as in "keep". Before "e" or "i", like an "s" ("th" in Castillian Spanish).
ch: Like the "ch" in "chocolate", "child".
d: Like the "d" in "dog".
f: Like the "f" in "filch", "Fokker".
g: Before "e" or "i", like the Spanish "j". Before other letters, like the "g" in "game".
h: Silent. If an "h" is between two vowels ("albahaca"), the vowels are elided ("albaca").
j: Like a hard "h" (ha,ha,ha), similar to the hard "h" sound in German (but usually not guttural). "Hu" followed by a vowel ("huecos", "Huancayo") tends to be pronounced like English "wh" (among those who pronounce "what" like "hu-wuht").
l: Like the "l" in "laugh".
ll: In most regions, like the "y" in "yellow". In the Río de La Plata region (Argentina and Uruguay), pronounced like the "sh" in "shallow".
m: Like the "m" in "milk".
n: Like the "n" in "now." Silent before "m" (inmigración, un médico).
ñ: Like the "ny" sound in "onion", "Enya".
p: Like the "p" in "pillow".
qu: Like a "k".
r: Beginning a sillable, strongly trilled (rolled), as is sometimes done in British English. Somewhat trilled when ending a word--for greater emphasis, it is trilled for a longer period of time, e.g., "saboRRRRR". In the middle of a sillable, pronounced like an English "d", as in "Adam".
s: Like the "s" in "savor".
t: Like the "t" in "torment".
v: See "b".
w: Usually only found in borrowed words like "whiskey". Often pronounced like "hu" (see "h" above).
x: Between vowels, like the "x" in "Mexico". Before consonants (e.g., "extranjero"), pronounced like "s". In Mexico, the "x" follows bizarre rules of pronunciation to represent sounds in indigenous languages, which is way beyond the scope of this writeup.
y: Like the "ll".
z: Same as the "s". In Castillian Spanish, the "z" is prounced like the English "th", as in "thistle".
There are many more flavorings and subtleties to Spanish pronunciation; for instance, The Real Academia Española considers "y" and "ll" to be two different sounds, but an explanation of "yeísmo", "lleísmo", and the like is a whole different writeup. These are basic rules that will get you through a day, but you'll need to get some audio material or go to the country of choice to really get a good idea.
As a rule, Spanish pronunciation should be much more definite than English pronunciation, since all the vowels are well defined. If you're American, please don't slip into the awful lazy habit of pronouncing things a la gringa: "may goostain las co-lories ee la dancing". I will remove your vocal chords in a dark alley.
Also remember the golden rule: If you can't pronounce it, use another word. I had a (native Peruvian) driver in Lima who was unable to pronouce the "tr/dr" sound due to a speech impediment. He said "labor" instead of "trabajo", "intentar" instead of "tratar", and "movilidad" instead of "transporte".