So, lets start this off with some basic tips for how to play Akshan;

First off, you'll want to use your Q, Avengerang, to take down the enemy minions pushing your way. However, you don't want to be doing this a lot at the start. The reason being is that you do too little damage with it (around a whooping 20 damage on both going out and returning) and, while the passive damage burst is good, it's not great against minions unless you want to pressure from the first second you're in lane. You'll want to be using this against the enemy champion instead, you're better off using it for minions around rank 3 of your Q so you can more effectively deal with the waves as they come in. Also remember your Q extends as it hits more targets, so aim it correctly and you'll hit the entire wave.

Initiating as Akshan should be started with your Q, not your auto. If you auto first, there's no guarantee you'll hit your Q. Your Q range is actually quite short, so open with it to get at least 1 stack of your passive and then get your 2-tap autos in, which should proc your passive damage burst. You'll kite a lot better that way.

Use his W, Going Rogue to roam into other lanes and get some more kills, or to bring back your allies. Remember, killing a 'Rogue' nets you a revive + some bonus gold, so doing this when you see an opportunity is usually worth it, just don't outright abandon CS at the same time, you still need minion gold (and preferably plates left on your tower as well.) Also remember you gain extra movement speed towards rogues which scales with W rank.

His Ult, Comeuppance, does a lot of damage to low health champs, but comes with a rough side effect that you must remember; he isn't Caitlyn. His Ult can be blocked by Towers, Champions and Minions. Only use his R when you're certain you can get a kill or apply a lot of pressure, otherwise it's just wasted.

His E, Heroic Swing, is an great dive mechanic and an even better initiate, as you rapid fire shots that can also proc his passive more than once if you're in range. However, be aware that champions and terrain (and terrain created by champions ((I'm looking at you, Trundle and Anivia)) block his swing. Don't let yourself be a sitting duck with it, or you'll have no option but to either Flash or just run like hell.

For his ability order, honestly, as long as you max your Q first and have at least 1 point in each ability, you're basically sorted. You'll want to max your Q, Avengerang first as you want both the damage it does and both stacks of his passive, Dirty Fighting.

Flash is a must have, no matter what. You'll need this in case you get ganked, or the midlaner you're fighting decides to CC you into low Earth orbit.

You'll also want Ignite just for that chase damage. It's also just standard to run ignite in place of anything else.

Exhaust can be swapped with Ignite if you wish, but it's only really handy alongside his E, which to be honest, on it's own is more effective than having Exhaust and no chip Ignite damage.

One of the only times I'll ever run Press the Attack is on Akshan, due to his passive. 3 auto attacks with Press the Attack, Blade of the Ruined King and Kraken Slayer can often knock enemies to half health into the mid game, which bearing in mind, coupled with Coup de Grace and his W, Going Rogue, you're going to be a roaming serial killer who...brings his friends back to life.

If you wish to swap Press the Attack, Lethal Tempo does also work, though I feel that's more for the Bot lane ADC's than the usual burstiness that exists in the midlane. Feel free to swap it if you think you'll prefer it.

This is what I build almost Every. Single. Game. You'll need all 3 of these items to realistically be effective.

Kraken Slayer is a must due to the 3 hit ability. Considering you'll be using Press the Attack and also using his passive, Dirty Fighting, your 3rd basic attack is going to hurt. Also adds attack speed that you'll 100% need, not just because he's a ranged AD, but his attack speed is lower due to his passive.

Berserker's Greaves is pretty standard, you can swap it out for Plated Steelcaps or Mercury's Treads if you must, but again, you'll need the attack speed more than anything else.

Blade of the Ruined King essentially buffs his 3rd hit proc, making it so you deal even more damage, but you'll likely need the boost in health damage when dealing with the support/tank (which you will be wanting to kill.)

On your first back, your priority will be Greaves, but if you've decided to run with Magical Footwear, or just wish to prioritise damage over movement speed (which you might, depending on the matchup), grab Noonquiver first instead.

Lord Dominik's Regards The Collector
You'll need these 2 items if the enemy tank(s) is/are running heavy AD protection. Remember that your passive + BotRK 3rd hit runs off AP damage, so while you can still deal damage with those, without these 2 items you're going to be slow taking them down without the added AD penetration.

Wit's End Phantom Dancer
These 2 items + BotRK make it so the enemy ADC/Mid/Supports are going to really struggle getting away from you, especially when used in tandem with your E, Heroic Swing. While this won't necessarily be priority, it can sometimes put too much pressure on them to stay in the fight, and once they're gone, these can help you keep up with the remaining enemy and get those tasty revives all Akshan players want.

So, let's go down the list and take a look at what you can potentially run for your 6th item, or swap some items out if you feel the need to do so.

Galeforce: Now, I tend not to use this that often, mainly because I much prefer the outright damage you can get with Kraken Slayer, but the main use case for it is to add mobility to his arsenal: Apart from Heroic Swing, Akshan has very little to no escape from fights, and even then, they can just walk into the way and block the swing entirely. The damage it does it helpful for chasing down as well, so feel free to swap this with Kraken if you feel like you need to, just be aware that sometimes it's better to have the damage and play a little more defensive.

Serylda's Grudge: Does very decent damage, especially against tanks, but the slow is actually very helpful. Slowing the enemy means more 3rd hits, more Kraken/BotRK hits, and overall more damage.

Bloodthirster: Really, you'll want to use this for sustain, and makes an excellent item if the builds above don't quite suit either of your needs.

So, this is my first guide on here, feel free to drop some posts in discussion and give it your vote, constructive criticism is very welcome and hopefully, this guide can help you out!