The Greeks were the first Europeans to learn to write with an alphabet, and from them alphabetic writing spread to the rest of Europe, eventually leading down to all modern European alphabets. Incidentally, the Greeks tried writing once before. Between 1500 and 1200 BCE, the Mycenaeans, an early tribe of Greeks, adapted the Minoan syllabary as Linear B to write an early form of Greek. However, the syllabary was not well suited to write Greek, and the exact pronunciation of Mycenaean words remains somewhat obcure. The alphabet, on the other hand, allowed a more precise record of the sounds in the language.
From the shape of the letters, it is clear that the Greeks adopted the alphabet the Phoenician script, mostly like during the late 9th century BCE. In fact, Greek historian Herotodus, who lived during the 5th century BCE, called the Greek letters "phoinikeia grammata" (φοινικήια γράμματα), which means Phoenician letters. You can see the similarities between the scripts in the comparision chart at the undefined page. Unlike Greek, the Phoenician alphabet only had letters for consonants. When the Greeks adopted the alphabet, they found letters representing sounds not found in Greek. Instead of throwing them away, they modified the extraneous letters to represent vowels. For example, the Phoenician letter 'aleph (which stood for a glottal stop) became the Greek letter alpha (which stands for [a] sound).
There were many variants of the early Greek alphabet, each suited to a local dialect. Eventually the Ionian alphabet was adopted in all Greek-speaking states, but before that happened, the Euboean variant was carried to the Italic peninsula and adopted by Etruscan and eventually Latin. The following chart compare various early variants, the Phoenician equivalent, the modern alphabet, and pronunciations.
Note: AP means Ancient Pronunciation whereas MP means Modern Pronunciation. These represent the phonetic values of the Greek letters in Classical and modern times respectively.
While there are many differences between the many variants of the early Greek alphabet, enough similarities exist to suggest the Greeks adopted the Phoenician alphabet once and splintered rapidly into local variants rather than adopting multiple times.
Early Greek was written right-to-left, just like Phoenician. However, eventually its direction changed to boustrophedon (which means "ox-turning"), where the direction of writing changes every line. For instance, you start on the right of the writing surfacd and writes leftward, and when you reach the leftmost end, you reverse your direction and starting writing toward the right. Even more confusing is that the orientation of the letter themselves is dependent on the direction of writing as well. In the above chart, the letters are drawn as if they were being written from left-to-right. If I were to write right-to-left, I would horizontally flip the letters like they were viewed in a mirror.
Boustrophedon was an intermediate stage, and by the 5th century BCE, left-to-right became the de-facto direction of writing. This change became standard in the Hellenistic world, and later in Rome as well, leading to the present day writing direction of Greek and Roman alphabets.
Greek letters were also used to denote numbers as well. They employed two separate systems, acrophonic and alphabet. The acrophonic system uses a few symbols to represent the numbers, as you can see below.
As illustrated in the above example the "one" numeral can be repeated as many as four times to get to the right number. To represent five, instead of repeating the "one" numeral five times, the "five" numeral is used instead. To represent numbers larger than 5 and less than 10, the "five" numeral followed by as many as four "one" numerals would be used. The same mechanism would be used for larger numbers.
The reason why this system is called acrophonic is because the numerals for 5, 10, 100, 1000 are the first letters of the Greek words for these numbers, namely ΠΕΝΤΕ, ΔΕΚΑ, ΗΕΚΑΤΟΝ, and ΧΙΛΙΟΝ.
In the alphabetic numeral system each Greek letter has a numeric value. In fact, letters no longer used at the Classic period such as ϝ (digamma), Ϛ (qoppa), and ϡ (sampi) continued to be used as numerals for 6, 90, and 900.
To mark that a sequence of letters is in fact a number, a special sign like a vertical dash or accent assign is placed after the numerals, ie σνζʹ which represents 257. To write numbers larger than 1000, a similarly vertical dash sign is placed before the numerals and below the line of writing, such as ͵αϡοϝʹ representing 1976.
The Greek alphabet is still a living writing system in Greece as well as Greek communities around the world. During its nearly long history, it was the basis for Etruscan (and by extension Latin), Coptic, Gothic, and Cyrillic scripts, as well as provided various degrees of influence on Glagolitic, Armenian, and Georgian scripts. In other words, the Greek alphabet was instrumental to the proliferation of scripts to write large number of vernacular languages in Europe and subsequently in many areas of the world.