Translation - side a'

Ἃλυς, Χανάν λούσων, ἀνάθημα ἦ, ἃρτι ῥήν δόρπον.

Νόα σάσσFω, Fάστυ ναῦς.

Ἁλιάς, Τηθύα, Χανάν λούει.

Νόα σάσσFω.

Ἀλύσσω, Κνωσό.

Nόα σάσων, δέ Fίπποις, μύλη νήτερμα, δέ μύσος, τιμήσειν, Θήβη FαFάζω, δέπας γάFι, Λάρσα κίει, Θήρα βᾶ ἃν, χάϊα ΔιFός, τύ δέχω ἂνυς, μύλη δέχω.

Δατινάσσει, σφέ βέβαμι, Fικάω.

Γυναί δύη, θεά ρυFείς, ἀραίFους σφείς.

In modern Hellenic the text is as follows: 

Άλυς, Χαναάν λούζοντας, αφιέρωμα πραγματικά, αμέσως αρνί φαγητό.

Πηγή συνθλίβοντάς με, πόλη πλοία.

Θαλασσινή, Τηθύα, Χαναάν λούζει.

Πηγή συνθλίβοντάς με.

Είμαι ανήσυχος, (στην) Κνωσό.

Πηγή αφού με συνθλίψει, πόλη πλοία, και στα άλογα, μυλόπετρα δίχως τέρμα, και βδέλυγμα, να τιμήσει, Θήβη φωνάζω δυνατά, ποτήρι γης, Λάρσα πορεύεται, Θήρα βασιλιά εάν, γνήσια Διός, εσένα δέχομαι την λύπη, μυλόπετρα δέχομαι.

Τραντάζει πολύ, αυτά έχουν βαδισθεί, έρχομαι.

Γυναίκα δυστυχία! θεά να ρυείς, παρακαλούνται αυτοί.

The English translation is as follows:

Alus, Canaan bathed, oblation really, right away lamb food.

Source squashing me, city ships.

Μarine, Tethya, Canaan bathes.

Source squashing me.

Ι'm restless, (at) Knossos.

Source after squashing me, and to the horses, millstone without end, and abomination, to honor, Thebe I cry out loud, bowl of earth, marches to Larsa, Thera king if, genuinely Zeus's, you I accept the sorrow, millstone accept.

It jolts a lot, these have been marched, I'm coming.

Woman misery, goddess be in flux, to them I plead.       

1. Just like in the linear B system the syllables containing the R letter can either represent the R sound or the L sound.
2. The u vowel does not exist in the actual Phaistos disk two letter per syllable phonetic hieroglyphs. Instead of this other vowels that were close phonetically were used, usually an i or an o. Here I have converted to syllables containing u's agreeing thus with the linear B system and helping viewers better make out the sounds.
3. One must take a look at the linear B system rules to understand for example how ka can represent the gamma and alpha letters, or the kappa and alpha letters etc. Unfortunately I cannot get into this type of information here.
4. This translation is from what most people call side B of the Phaistos disk(helmet shaped symbol at center). As one can deduce from the translation this is actually the first side of the disk.
5. Alus, Knossos, Thera, Thebe, and Larsa are all place names. Thebe or Ogygia or Thiva or Thebes or Kadmeia is the mythical Boeotian city inhabited from Neolithic times, birth place of Dionysus and Hercules. Larsa is either the Sumerian city or a different pronunciation of the acropolis of Argos(Larissa). Thera is the island of Sontorini in the Cyclades. Tsikritsis reads the place name sa-ru in Linear A'. Here sa is the aspirate alpha sound so in our Phaistos disk case it is depicted as 'a'. The place name is thus Alus. 
6. Tethys was an ancient Hellenic sea goddess.
7. The phrase "oblation really, right away lamb food" seems to mean that he or she intends to present an offering to a god or goddess of lamb and other food.
8. The radiation source is the volcanic eruption(Thera volcano ~ 1630 B.C.). Source is a volcanic source, a source of lava. The word squashing emphasized the destruction(city, ships) caused by the eruption, and the loss of life(horses). Millstone is volcanic rock, in other words dry lava. The word abomination probably refers to filthy volcanic ash. The "without end" phrase means "all over the place".
9. The phrase "to honor, Thebe I cry out loud" probably implies that the homeland of the Phaistos disk creator is the 7-gated city of Thebes. This means that the disk and probably the hieroglyphic writing system it encompasses did not originate from Crete, it originated from mainland Hellas. Maybe that's why unlike Linear A', the Phaistos disk text - once decoded - is so easy to translate. 
10. The phrase "bowl of earth, marches to Larsa" means that a mushroom cloud of volcanic ash and debris was  carried by the wind in the direction of the city of Larsa(probably Argos). The phrase "It jolts a lot" informs us that earthquakes following the volcanic eruption.
11. The peculiar phrase "these have been marched, I'm coming" might refer to a distance encoding(source to destination) of some kind encompassed on the disk. 
12. The phrase "Woman misery, goddess" might refer to the goddess(woman), Tethys and the misery brought forth by the tsunami.
13. The phrase "be in flux" means to flow. Maybe it refers to the flowing of the sea goddess Tethys.
14. The phrase "to them I plead" probably refers to the rulers of Phaistos.