Ahri is a mobile burst-ranged assassin. She can look for picks and burst people down with charm easily. Sadly, her damage output is low compared to other assassins/mages and her AP ratios aren't super strong either. She relies on getting fed early to midgame to make an impact in the late game. Otherwise, she just becomes a charm bot.

In the early game I usually take W first. Then I autoattack and W to proc electrocute on my opponent, which takes a lot of their health away. Level 2 I take Q then go in for another trade with Q and W. (Autoattacks as well if they are melee). Level 3 I usually go for an all-in with charm and Ignite for a First Blood or early kill.

Focus on farming and poking. Once your opponent is low enough, go for the all-in.

Champions become really easy to kill when you have ult up. Get them a little low by poking, ult in and out, and they're dead.

Roam a lot as well. Ahri is pretty good at roaming, especially with ultimate, and she relies a lot on early kills to maintain a lead. Fight for drag and for Herald. The odds are in your favor if you land charm.

By midgame you should have quite a lead. Look to take first tower at mid, then you can start roaming and teamfighting a lot more. Roam to look for picks, if there's nothing to do just come back to mid or help losing lanes. For sure you want to fight for objectives. If you have ult up you can split push a bit for the exp and gold, but not too much as you aren't a splitpusher and Ahri will almost always die if more than one person comes to kill you.

Sadly, if you are behind, just look to play passive, stay in lane, and farm a lot. Maybe take first tower while everyone is roaming and teamfighting. You will be useless in teamfights anyways. Once you get your mythic you should be able to make a come back. If you're behind in deaths, just farm so you will be equal in gold and items.

Ahri falls off lategame, sadly. Try to buy Magic Pen if you aren't bursting your targets fast enough. Look to splitpush with your ult up (and it should be on like a 60 second cooldown by the lategame). In teamfights, engage with charm then kite backwards as you spam Q and W. Ideally you want to finish the game before late game approaches.

When fighting for objectives, the cheesiest tactic you can use is the classic "hide-in-a-bush-and-charm-unsuspecting-victims" method which will land you a lot of kills.

As Ahri, try to charm the tank at the front, then ult to the backline and use Q and W to oneshot them. Be careful of your positioning and try to stay behind your tanky champions at all times.