Gangplank is one the BEST crit champions in League of Legends. He is not an OP( Overpowered) champion as he is very squishy. So, do not be the one to initate any fight, but don't be too passive to not chase and kill somebody. Credit goes to Takionix for typing this for me.

Gangplank is not an early game character, though if you have the runes that I suggest, you might get a few lucky kills, but understand that Gangplank is a mid-late game champion. When you begin the laning phase, I suggest you get one point in parrrley and then two points in remove scurvy for survivability. Notably since Gangplank has a good healing ability, you may wonder why you would get two health potions at all, but if you've played Gangplank, you'd know it is a 20 second cooldown on Remove Scurvy, therefore, you should not rely on that in the beginning of the game to save you. Use your speed to your advantage.

Mid Game with Gangplank is from about level 6-13. This is the phase in Gangplank that I call "Mapstalking." You should always be watching the map and seeing where your ultimate could help in a teamfight. Keep in mind that your ultimate slows, so if you are to use it, place it slightly in front of them and not directly on top of them for the maximum chance of damage and the most slow. When you do this, it also forces them to make a choice between the ult or go towards the people that are already attacking them. This almost always guarantees that you will kill them. Gangplanks ult is very good, but the drop area of the cannon balls is random, so don't expect to cast your ult on somebody with low health and kill them because somebody can walk all the way through your ult and not get hit. Parrrley is the skill you want to max out first because you can use this to harass easily. Before a teamfight actually starts, you will want to harass them with this. When Gangplank is fully built, he crits with around 1000 with this. When a teamfight ensues, your ult has a good crowd control and area of effect usage. When a teamfight starts, cast your ult on the area with the most people. Then use raise morale to increase your own team's attack damage and movement speed. There may not always be a minion there to activate it, but movement speed and attack damage are always a plus. One of Gangplank's weaknesses are burst/stun characters such as Evelynn, Ryze, Pantheon, and Annie. So, be extra careful when playing against these characters. Parrrley can be blocked by Pantheon's shield. Remove Scurvy removes crowd control effects and stuns on you.

Late game GPs are very good carries. Say you're down to 1100hp but your max is 1700(Just an example) , use remove scurvy... even though it seems like a waste of healing because the teamfight hasn't started yet, during the teamfight you will have another chance to use remove scurvy. In other words, use remove scurvy whenever possible and if necessary. A lot of times, there will be creep waves that might kill towers. You can cast your ult over a turret that has a lot of minions over it in order to get around 200 gold and makes it so nobody has to leave the teamfight. This is not a waste of ult even though "OMG HE ULTED ON MINIONS!! NOOB" because you farm minions, and defending turrets is more important than getting kills.

Grog Soaked Blade (Passive)- A very good passive if you want a lot of kills, though with this build it can only be activated with normal attacks (right-clicking). This poisons the enemy. It's not a lot of poison, but it does do a considerable amount of damage and will get you some kills.
Parrrley ("Q" Skill)- Max this out first. A ranged attack that if you kill somebody, a monster, minion, or champion, you gain extra gold. This is good to last hit with. You can gain 16 extra gold per minion if you last hit with this. This helps you farm very quickly. This move also increases your crit damage.
Remove Scurvy ("W" Skill)- THis is a heal/ remove crowd control effects. This should be your second skill to max out. Without any AP added to it, it heals for 380. Remember, any moves that stop you, are removed after casting this. This is why I don't get Banshee's veil.
Raise Morale ("E" Skill)- Though this skill shouldn't be maxed out first, it is still useful. This is good for chasing or harassing. If enemy champions are killing a minion, kill that minion in order to creep deny them. If you keep doing this, you will deny about 20-50 creeps for them. This denies them EXP and Gold constantly. The effect given from this skill is not that long. Do not rely on this skill too much.
Cannon Barrage ("R" Skill)- This is your ultimate skill. Like I described earlier, this is a barrage that can be cast anywhere on the map. This ult is very versatile. Like I said earlier, you should always be watching the map and seeing where your ultimate could help in a teamfight. Keep in mind that your ultimate slows, so if you are to use it, place it slightly in front of them and not directly on top of them for the maximum chance of damage and the most slow. When you do this, it also forces them to make a choice between the ult or go towards the people that are already attacking them. A lot of times, there will be creep waves that might kill towers. You can cast your ult over a turret that has a lot of minions over it in order to get around 200 gold and makes it so nobody has to leave the teamfight. This is not a waste of ult even though "OMG HE ULTED ON MINIONS!! NOOB" because you farm minions, and defending turrets is more important than getting kills. You can also use this ult to help a teammate run away. Place this so they have to run into it in order to chase the teammate. It is ALWAYS appreciated when a teammate saves another teammate.

Greater Mark of Malice- This makes your early game easy and you crit for about 180-170. Very devastating to people that start with 400HP. This does help late game aswell.
Greater Seal of Malice- Same effect as with marks.
Greater Glyph of Replenishment- GP eats mana quickly, even late game. Remove Scurvy will deplete your mana.
Greater Quintessence of Replenishment- This also helps you regenerate mana.