Not Updated For Current Season
Start with cloth armor and defense curl, and don't die early. Run when you need to, and get boots asap. Use Powerball then defense curl then tremors for fights once level six. Force the opposition to run b and then push the tower, as Rammus is THE tower killer. Hop into the jungle and get the blue buff, otherwise you'll be going b for Mana very often.
During team fights it's best for you to be the first one in. When the opposing team are all pushing one lase, ping them, then Powerball into them, pop defense curl and tremors, then taunt the squishy when he tries to run. Your team should arrive just in time to steal a kill or two, and help as you kill the rest. When powerball refreshes, chase down the last of the opposition if there are any left.
Even if your team sucks, as long as one or two people come to the ping, you are guarenteed at least one kill.
This is a very aggressive playstyle, and won't work for some people.