Not Updated For Current Season
Rammus is a survivor, and in order to survive he needs the proper items. First things first, the purchase of the Ninja Tabi are necessary. Followed by Sunfire Cape, Thorn Mail, Sunfire Cape, Nashor's Tooth, and if the other team is still going strong Guardian Angel. You can also sub a third Sunfire Cape for Guardian Angel depending on the other team. I suggest Nashor's Tooth because having the AP helps with his Tremors attack, as well as the Power ball. I have been none to get Abyssal Scepter as opposed to Nashor's tooth, just depends on the strength of the other teams Champions.
In the beginning, you will want to farm as much as possible, because you will be pretty squishy, will be good to have someone with Range to team up with. (Lvls 1 - 7)
Mid way through the stage (8-12) try to farm for a little while longer, but ganking is always a big help. Providing support for your team is best, you can start taking a lot of damage, but you can't hang in the mid to much.
The last part of the game, you should be a heavy tank, able to take towers, and stay in the middle of the fight, taking most of the damage while your teammates are attacking outside.
Use your Defense Ball Curl as much as possible, it doubles all your defenses, and helps out in a pinch. If you see a teammate being attacked, Taunt them and take the damage, and allow the mate to get out, and the Flash your way out of harms way.