Aggro : Non stop destroy your face ASAP. Example decks include Faice and Aggro Reva, cards include Saberspine Tiger and Flameblood Warlock
Tempo : Wants to gain board momentum and use it to bash your face in. Uses solid value cards to gain and keep momentum. Decks include Tempo Lyonar. Cards include Bloodtear Alchemist, AoE card.
Midrange : Kinda half way between Aggro and Tempo, keeps up momentum and wails on you down to a small bit of hp left and then bursts it away. Decks include Midrange Lyonar, most Vetruvian Obelysk decks also tend to be rather midrangey in their playstyle.
Combo : Relies on a specific set of cards that combo to create a high damage output that finishes the game that turn, preceding turns are usually light control and chip damage with heavy draw power. Decks include Meldhai and ArtiVet. Cards include Mirror Meld, Auroras Tears, Time Maelstrom, Spelljammer, Heaven’s Eclipse.
Control : Slowest playstyle, aims to control board through very efficient removal spells and AoE while also delaying with high healing power until they’ve exhausted most of their opponents resources at which point they begin to crush you with heavy minion after heavy minion. Decks include Control Magmar(haven’t seen that one in a while), Control Faie, some slowet variants of Healyonar. Cards include Thumping Wave, Enfeeble, Plasma Storm, Sundrop Elixir, Punish, Silithar Elder, Variax, Nosh-rak, Meltdown.
Ramp : Aims to cheat big minions out by reducing their cost. Decks include Bigbyssian(only variant I’ve seen be nearly successful, not sure if Rampmar is any good). Cards include Darkfire Sacrifice, Flash Reincarnation, Arcane Devourer, Spectral Revenant, Silithar Elder, Vorpal Reaver.