A good subtitle for this post would be “How to get from 10 to 5 without dividing by 2.”
Latin had ten vowels: long and short a, e, i, o, and u. The long vowels were literally “long”: they were held about twice as long as their short counterparts. Classical texts didn’t indicate vowel length, but Latin textbooks, dictionaries, and the like use a macron (as in ū or ē) for long vowels, and sometimes also a breve (as in ŭ or ĕ) for short vowels.
As discussed in an earlier post, Spanish has only five vowels: just plain a, e, i, o, and u. Wouldn’t it have been tidy if each each long and short pair in Latin had collapsed into a single Spanish vowel? In fact, the three Latin pairs ē/ĕ, ō/ŏ, and ā/ă did just this, becoming Spanish e, o, and a. But Latin i and u split apart, with their short members absorbed into Spanish e and o, respectively.
These changes are a lot easier to grasp in table form (click for a better view):
This table overlooks a crucial detail: in stressed syllables, Latin’s short ŏ and ĕ became the Spanish diphthongs (two-vowel sequences) ue and ie. This may sound like a mere, dry, or even boring technicality. But in fact, these diphthongs are a big part of the sound of Spanish. Appearing in tons of core vocabulary words, like puerta and fiesta (from Latin pŏrta and fĕsta), they distinguish Spanish from its Romance cousins: compare French porte and fête, and Italian, Portuguese, and Catalan porta and festa. The Latin short/long difference also explains Spanish “boot” verbs, whose root vowel diphthongizes when stressed, e.g. nIEgo vs. negAmos, or pUEdo vs. podEmos. These verbs had a short vowel in Latin: negar comes from Latin negāre, and poder from Vulgar Latin potēre. Verbs with stable vowels, like deber and poner, had a long vowel in Latin (dēbēre and pōnere).
This is why you can’t tell from an infinitive which verbs have the “boot” pattern: the crucial vowel difference has been lost. To make matters worse, over time some verbs have drifted, either taking on the boot pattern even though they had a long vowel in Latin (e.g. pensar, from pēnsāre), or becoming regular even though they had a short vowel (e.g. sorber, from sorbēre). The moral of the story: Look it up!