Relatively simple as with most Heroic decks. Cast heroic creatures, cast spells on these creatures to ramp them up and bash in face. Due to most of the deck having to work with a combination of cards (creatures and spells to cast on them) there is very little in the way of board control, and you generally run out of gas quickly. We try to avoid the board by becoming unblockable, and run a few cards that replenish themselves to have more lasting power.
Creatures
Your creatures are the important beaters in this deck. Without heroic creatures you have no chance of winning.
Favored Hoplite has a nice ability that makes it invulnerable (not indestructible) when targeted with an instant, leaving you to use the protection spells for your other creatures.
Battlewise Hoplite
helps you with fixing your draws, which is very important as to not flood yourself with just creatures or spells targeting creatures while you have none to cast them on.
Phalanx Leader is very white-intensive, but will help you greatly to close games once you've built a little board.
Battlefield Thaumaturge significantly lowers the cost of important sorceries/instants to 1, and enables your Apostle's Blessing to be cast for only 2 life and 0 mana! It's heroic doesn't give counters, but hexproof, which means you can use any spell to save this dude from targeted removal, and save the protection spells for your other creatures.
A single
Fabled Hero
is there to either get through and win the game (usually on the spot) or draw away opponent's kill spells because of the potential damage.
Abzan Falconer
is NOT a heroic creature, but does very well in providing evasion for all your heroic creatures. It can be exchanged for Ainok Bond-Kin, whose First Strike will almost always mean that the opponent can't trade into you with creatures, but without trample it's better to just hit face.
Non-creatures
Apostle's Blessing is the all-star, providing protection from whatever you want. This prevents those pesky opponents from targeting or blocking your creature. Oh and did I mention that Battlefield Thaumaturge makes it cost 0 mana? Yes, I did.
Emerge Unscathed does the same for all colored spells, TWICE. Which also means double triggers for heroic.
View from Above
is a perfect idea I took from the deck that I based this one on. Since you'll almost always have a white permanent when you cast this, this is a recurring heroic trigger which gives your creatures flying evasion. With Thaumaturge it costs just 1 mana.
Hidden Strings is also inspired by that original deck. Cipher it on a creature that you get through reliably (for example with your other spells), and get 2 triggers + pseudo vigilance every time you hit (untap your own creatures, tapping opponents is not useful after combat).
Distortion Strike for double unblockable beater, or you can get in a combination of Launch the Fleet and
Icy Blast
which both cost 1 mana to target the entire field if combined with Thaumaturge. It's relatively easy to use Icy Blast's ferocious as well (eventually targeting one of your own creatures to get to 4 power and then swing with all the rest next turn). The Fleet going wide synergizes perfectly with the Phalanx Leader.
Ordeal of Thassa draws you cards. Due to heroic triggers it will either take 2 turns or only 1, making it effectively a draw 2 for 2 mana sorcery. Very useful considering we want to be attacking almost every turn anyway.
Triton Tactics in the sideboard against other aggressive decks. This slows them down and lets you through, while giving you temporary high toughness.