Below are several suggestions going from least to most harmful for the coin. While most people say you should never clean a coin, I'd say that's true for a key-date, but you have to weigh the fact especially with a common date, like you have, that the coin has already been environmentally damaged. Do you want a good looking or bad looking environmentally damaged coin. I really doubt that options 1 to 3 below would lower the value any of an environmentally damaged common date coin. They may make it more desirable if it looks better, particularly to you. I oftentimes use #3 on most Indian Heads I find with great success.
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1) If you want the least invasive cleaning -- soak it in mineral oil. It will do the exact same job as olive oil, but olive oil can go rancid. If there is some olive oil on the coin when it goes rancid, it will corrode the coin. If you leave some mineral oil on the coin, it wont harm the coin. If it's got a nice green patina, leave the patina.
2) If you want a slightly more invasive route, soak as above and rub coin with q-tip once a day to get any surface debris/ corrosion off.
3) If you want a more invasive route, then (don't put the coin in hot hydogen peroxide!) -- microwave some peroxide and dip a toothpick in the peroxide and scrape lightly the surface of the coin being careful not to remove any of the green patina and also being careful not to chip the rim of the coin. (This method works great for cruddy IH's but still preserves the patina). IT takes the most work and patience -- you may need to spend 45 minutes on 1 coin depending on how clean you want it. Also, make sure if you do this, after every 30 seconds or so to wipe the peroxide off the coin (as well as loosened crud) with paper towel so as to not let it inadvertently eat the patina away.
4) If you are lazy, you can buy an acid based coin cleaner like nik-a-lene, but this will most likely damage the coin more than you want.
5) If you are super lazy you can tumble it in a rock tumbler and it will damage the coin more than you want.