It all depends. I would start with a little warm soapy water and a toothbrush. Then if I wasn't satisfied I would put it in olive oil to soak for a day or so. Others will tell you that olive oil is bad because it (the relic) will leak oil for along time afterwards and tell you to use hot/warm hydrogen peroxide.
I've tried the peroxide, and didn't like the results on an old copper flat button (oxidized it and turned it a funky green that won't come off) so I haven't used it since. I've come to the conclusion that it depends on the soil condition that the relic has sit in over the last 100+ years.
Also, it depends on what kind of "dirt" is on the button. Around these parts you sometimes get a sand "cement" that just won't come off. I've taken wire brushes to them and been fairly happy with the results, but it does damage the button... But if you got the cement muck, then its better to see some details than none at all I suppose.