In the US, according to a seven-year study by Network for Good of online-giving behavior, 22 percent of all online gifts to charities are made in the last two days of the year. These two days of giving cap off the month of December when charities receive one-third of all their online donations. http://goo.gl/6LrgA
How? First check out the organization website. I didn't find many genealogy/family history societies that could accept a donation online, but maybe your's is one.
I look to the charities I support to be effective. My guide is Charity Intelligence Canada, which for whatever reason only names one Ottawa charity, The Ottawa Food Bank (pdf). Cash goes a lot further than the food you drop off in the supermarket collection bin, and you get a charitable receipt.
There are many other options, local, national and international. Remember to help your good cause before the end of the year if you can.