EARLY TO MID GAME!
During laning phase, you want to trade efficiently with your enemy, avoiding extended trades due to Cassiopeia's low base mana pool. You can easily use Noxious Blast on the enemy when they walk up for CS, as they must stand still for a split second to AA. Before you get Tear of the Goddess (if you chose to start with Doran's Ring or Corrupting Potion, you want to use your mana sparingly. You can use Twin Fang to last hit minions, and farm towards your tear. You should use proper wave management by freezing the wave near your tower, so you're not at risk of being ganked, and make sure to put a ward nearby. Cassiopeia is immobile, so be wary of using your Flash, as you have no surefire escape after - she is an easy target to gank.
Cassiopeia has good push potential, and roam potential. You should push when optimal and look to gank other lanes - you can even gank normally ungankable lanes such as Ezreal as your Miasma grounds the enemy, rendering their dashes or blinks useless.
When you get Tear of the Goddess, you want to be stacking it as quickly as possible, last hitting with Twin Fang, and trading aggressively with the enemy. Conqueror is very strong on Cassiopeia as she can stack it very fast with her low cooldowns. This provides us with a large chunk of AP and also heals us for 8% of all damage dealt to champions, meaning we can easily stay sustained during prolonged trades
MID TO LATE GAME!
During this point, our Archangel's Staff should be transformed into Seraph's Embrace, and we generally have an unlimited mana pool. If you've been CSing correctly, or getting kills, you should have Rylai's Crystal Scepter, which slows the enemy on all your abilities - basically a permaslow for Cassiopeia, and you can look to play aggressively. Cassiopeia's damage is generally unmatched during mid game, she can shred through targets with ease, and keeping them slowed and grounded while she runs (slithers?) them down.
Focus on helping out with objectives as much as possible, you can shred through the Dragons, and the changes to them in Season 10 make them all the more important and impactful.
Cassiopeia has an extremely strong late game, she can tear through any single target with unmatched speed, and has the capability to have a full, 6 item damage build due to not needing to buy boots. Cassiopeia wants to be with her team and set up big teamfight ultimate's, especially if the enemy decides to facecheck a brush while you're hiding as 5. This will guarantee you a stun off Petrifying Gaze and can in turn win you the game. Make sure to keep Miasma on the ground, locking enemies down and finding ample opportunities to use your ultimate. Even the slow is useful, so don't hold it to find that picture perfect, YouTube worthy 5man stun!
