Toothpick it. That's it. Do it slowly, and don't dig. There are a few good videos on YouTube on how to clean large cents, watch the one where the guy uses three different LC's and three different methods.
Don't use water - it'll destroy the details and the coin will look like crap when you're done.
Don't use olive oil - it might eventually remove some dirt but the coin will be so dark it'll be ugly.
My best large cents are the ones where I left some dirt on them, in between the high points. It makes the details pop. Shows the highlights.
Remember: once you've taken the dirt away you can't put it back.