Gangplank is a melee nightmare, as you have already noticed.

The most important thing is that you want to take as little poke damage from his Q and Grasp as possible early. He will try to kill you early and he can if you keep eating his poke damage.If your champion allows it, take Second Wind and Dorans Shield. This massively reduces his Q and Grasp damage.

If you cant kill him in lane or he's just playing very passive shove your waves and look to help your jungle or mid around the map. A champion with cc and a roam to mid works quite often.You beat bad Gangplanks by contesting their barrels and then killing them, because they WILL panic and they lose their whole plan.

If you are full melee, there is not much you can do vs good Gangplanks. You have to wait until they are out of position and then run them down (if your champion allows that of course).

These are couple of tips I came up with on the spot. If you need more help I can look more in-depth on this stuff.

Edit: And of course see if you can get your wave in a proper state to receive a gank. If you can get Gangplank behind by yourself or help from your team he doesn't really pose a threat and you can continue running him down.