I spent a month this summer teaching English to kids in the Basque Country (Euskadi), and I noticed that the locals have great trouble pronouncing or differentiating many English vowel sounds. This is really not surprising. Spanish, amazingly, makes do with just five vowel sounds in the whole language. Only five! This level of simplicity is almost inconceivable for those of us coming from languages like French or English, where depending on accents and how you count them, we distinguish something like 17 different vowel sounds. The Italians and Basques pull off the same trick as the Spanish, with much the same sounds, and that is true of many of the other dialects/languages found around the Spanish state, too, so this guide is for them as well.

Here are some of the vowel sounds which I find cause most confusion for speakers of Spanish, and make their accents most obvious. A stroke (/) between words indicates that a distinction is being made; two words separated by commas (,) provide examples of the same vowel sound. Symbols in square brackets are from the International Phonetic Alphabet, and you don't need to worry about them if you don't want to. Note that these guidelines are based on my own accent, which is that of a middle-class Londoner. This is something close to what's known as 'Received Pronunciation', but with a touch of 'Estuary English'.

  • Bean/Bin
    The ea in bean [iː] is more-or-less like a Spanish i [i], maybe just a bit longer. 'ee' and 'ea' are almost always pronounced like this, and sometimes 'i' is too. The i in 'bin' [ɪ] is a different sound, made by moving the tongue away from the roof of the mouth, and it is short. I use a longer version of the same sound [ɪː] when I say 'beer'.
  • Bun/Barn/Bang/Ban
    The 'u' in 'bun' [ʌ]/[ɐ] is close to the Spanish 'a' [ä] but shorter, while the 'ar' in 'barn' [ʌː] is the same sound but longer. The 'a' in 'bang' [æ] and 'ban' [æː] is a different sound. Where the sound in 'barn' is the sort of noise we might make when sighing contentedly, the 'a' in 'bang' is more like the noises we make when crying in pain - the tongue is pushed up towards the roof of the mouth.  The 'a' in 'ban' is a long version of the same sound. Strictly speaking the Spanish 'a' falls in the middle of these sounds, but it is probably closest to the one in 'bun'. 
  • Burn, Her
    'Ur' and 'er' here represent the sound [ɜː] made by zombies and confused English people. There is nothing like this sound in Spanish, but if you make a Spanish 'u' (which is like the English 'oo' in 'boon') [u] and then completely relax your lips and maybe open your mouth a bit wider, you should be able to make something similar. Some North American accents omit this sound entirely, and just make a long 'r' sound.  
  • Bonk/Born/Bone
    The 'o' in 'bonk' [ɔ] (and the similar sound in 'born' [ɔː], which is about twice as long) is close enough to the Spanish 'o' [o] that you can get away with it, but it's made without rounding the lips, and slightly further back in the mouth - you might find you can get there by moving your tongue back a little bit. The 'o' in 'bone' [əʊ] sounds even closer to the Spanish 'o' to most people, but it's actually a diphthong - it's the 'er' sound above, quickly sliding into a 'u'/'oo' sound. It passes through [o] in the middle!
  • Beneath, Behind
    The first 'e' here is known as a schwa sound [ə], and it turns up a lot in English. You can find it spelt with any vowel and many different letter sequences, because it represents something like a failure to pronounce the original sound when a syllable isn't stressed. Not very helpfully, sounds which are usually rendered as schwas get the original vowel sound instead when they are stressed, so 'an elephant' is said with a 'ə' sound, but 'an elephant' gets an 'æ' instead. This is understandably a source of confusion for most foreigners, especially those used to languages where every vowel has a single well-defined sound associated with it. The schwa is pronounced with less emphasis and definition than anything in Spanish - try to put as little effort as possible into producing it, and you should be able to get somewhere close. Relax your tongue, relax your lips, don't put too much voice into it. In fact, if you can avoid saying it at all, you're most of the way there: "b'neath 'n el-ph'nt's b'hind".
I hope this guide will be useful for people learning and teaching English. I haven't attempted to be comprehensive here - these are only the vowels that I have noticed being particularly problematic for Spanish speakers, but do let me know if you think I have omitted anything important.