Basque pronunciation is quite straightforward and easy for native speakers of English and most Western European languages. As with all languages, there are various dialectical variations in pronunciation, of which only a few should really be noted by the learner (the rest being much more localized phenomena that are peculiarities of specific dialects).
Batua, similar to Spanish, has five distinct vowel sounds: a, e, i, o, u. Vowel length is not phonemical (i.e. you can't distinguish between words based exclusively on the length of a vowel) and vowels should always be pronounced clearly and crisply, not weakened into a schwa (the vowel in the word the) or ellided completely. The vowel sounds are:
[a] as is father
[e] as in get
[i] as the ee in beet
[o] as in don't (but note here that in NA English, we have a tendency to pronounce this with a w at the end, which is not done in Basque)
[u] as the o in move
There is also one diphthong (combination of a vowel and semi-vowel) that is represented by the digraph (two letters) eu. It is pronounced like the e sound quickly followed by an English w. You'll have lots of practice of this sound, as it occurs in the name of the language: euskara.
Again, the vowel ü might occur in some of the northern dialects, but not in the standard Batua. It is pronounced like the same letter in German, or the French u.
Here, again, there is a remarkable amount of overlap with the English system of consonants. For this reason, it is probably best to concentrate on differences, rather than similarities. In this way, it is easier to focus on getting the few unique sounds down correctly rather than trying to memorize the entire system.
g is always what linguists call a stop, and what most non-technical books call hard. That means that even before e and i, it is pronounced like the g in go. Note that some people also do what is done in Castillian Spanish and use a sound represented by the Greek gamma γ whenever g appears between vowels. This sounds similar to the Parisian gargled r. Even if you don't use this sound, however, your Basque will be neither incomprehensible nor strange-sounding.
h is generally silent in the South (Spanish areas) and is pronounced just like in English in the French areas.
j is either pronounced like the y in yes or like the Spanish j, which is similar to the ch in Bach in the southern part of the Basque Country. In the northern part, it is pronounced like the s in pleasure. However, six different pronunciations for j have been counted in modern basque dialects (j, dʒ, x, ʃ, ɟ, ʝ).
ñ is pronounced the same as in Spanish: like the ni in onion.
r is, for the most part, a short tap when it occurs anywhere other than at the beginning of a word, much the way it does in Spanish. You will likely notice that it sounds just like the Parisian r when people from the north speak Basque; I am not sure if this is just the effect of French pronunciation on Basque, or a feature of the northern dialects themselves.
rr is a trilled r, similar to the one in Spanish. It comes from the back of the throat, not the front (as in Italian). Note that this is also the sound of a single r when it occurs at the start of the word.
s is probably the trickiest sound of all. It is not like the English s, but rather like the one used in Castillian Spanish. It sort of sounds like English sh, but is much softer. In effect, it is produced by putting the tip of your tongue at the back of your top front teeth when saying s. It takes a bit of practice.
x is pronounced like sh in ship.
z is always pronounced like s in silent and never like z in zoo or pizza.
One last feature of Basque that should be mentioned is called palatalization. This occurs when a sound like n or l has a slight y sound tacked on the end. In Basque, it might be represented by the special characters ll or ñ, but it could also occur because an i either precedes or follows the letter l or n, as in koilara, which means spoon.