The Latin alphabet wasn’t just invented one letter at a time but rather borrowed wholesale from the Etruscans (Rome’s neighbours to the north), about 700-600BC.
Or at least, most of it was.
To cut a long and very interesting story short, the Romans got the alphabet from the Etruscans, who got it from Greek traders and settlers in Italy (about 700BC).
The alphabet borrowed by the Etruscans was a Western Greek variant of the early Greek alphabet, which the Greeks had borrowed and adapted from (almost certainly) the Phoenicians (a great maritime people from modern Lebanon) in 900-800BC.
The Romans borrowed these letters from the Etruscans:
ACEFHIKLMNPQRSTV
and borrowed BDOX either from the Etruscans (who didn’t generally use those letters but had definitely borrowed them from the Greek alphabet) or directly from the Western Greek alphabet.
In the very early Roman alphabet, C had to serve for both of the sounds /k/ and /g/; but by adding a stroke to C, they removed this ambiguity and created a new letter G; K faded largely out of use.
Later, during the Republic, when the influence of classical Greek learning was great and Latin was importing a large number of Greek loanwords, YZ were imported.
Later still, the letter V, which could stand either for an /u/ vowel (as in ‘cool’) or a consonant which was originally pronounced rather like an English ‘w’ but which later changed its pronunciation to /v/, was adapted by doubling to represent /w/ (about 300-500AD).
Finally, U was added to distinguish the vowel /u/ from the consonant /v/, and J (a variant of I, originally with the sound /y/) was added for similar reasons, in the early Middle Ages.
Of course, a wide variety of other letters exist in alphabets descended from the Latin alphabet, but that’s the story of the 26 English ones.
http://www.ancientscripts.com/latin.html
http://www.wikipedia.org/wiki/Alphabet