THE BRAIN TRUST: Daenerys is flanked by her closest advisers; Tyrion Lannister, Varys, and Missandei.
THE UNSULLIED: Grey Worm and the rest of the Unsullied are on board, naturally. Dany originally had 8,000 Unsullied when she liberated them after sacking Astapor, though it's not specified exactly how many are left after her many conquests and struggle against the Sons of the Harpy. Nevertheless, they're an elite fighting force.
THE DOTHRAKI: Dany's Khalasar, consisting of about 100,000 Dothraki, are crossing the "poison water" in "wooden horses," just like they promised to Khal Drogo way back in season one. Another shot shows that they've brought along their horses, which make sense.
THE GREYJOYS: Yara and Theon Greyjoy, along with the 100 ships they managed to swipe from the Iron Island fleet, are with her too, having promised to ally themselves with Dany in return for the Islands' independence (and maybe some help killing their Uncle Euron).
next slide will load in 15 secondsSkip AdSkip AdELLARIA SAND: A wide shot of the fleet shows that Dany's got the Dornish navy on her side, having allied with them after Varys sailed to Sunspear to make an agreement with Ellaria Sand. The ships, emblazoned with the Martell sigil, must have sailed to Essos to meet up with the rest of Dany's forces. Varys hitched a ride back with them, presumably.
THE TYRELLS: Another shot shows that the Tyrells have also joined the fray. Varys was able to form an allegiance with Olenna Tyrell, the Queen of Thorns, while he was in Dorne. Both the Tyrells and the Martells have a serious grudge against the Lannisters.
THE MASTERS' SHIPS: Many of Dany's troops are on the ships that she took from the Masters after defeating them during the Siege of Meereen, now sporting sails with the Targaryen sigil and the flagships sporting impressive dragon mastheads.
THE DRAGONS: Dany's three dragons, now seemingly fully under her control, are flying along with the fleet.
It's hard to make an exact count, but the final shot of the season seems to show upwards of 350 ships (and three dragons) in Dany's fleet. They're packed with some of the fiercest fighters in all the world. Westeros won't know what hit 'em.