I can't say specifically about charities to help Greece. If someone on here has specific knowledge, please chime in.
The only shortcut I know to tell if a charity is legitimate is to consult one of the ratings/watchdog type groups that monitor charities. For example, for explicitly Christian charities, there's a group called the Evangelical Council for Financial Accountability. To be a member in good standing a charity has to meet a bunch of criteria, like having an independent board of directors, i.e. you can't start a charity, make yourself the president and your brother-in-law the vice president and you're not answerable to anyone else; their fund-raising and administrative costs can't be more than a certain percentage of total income, etc. There are similar groups with similar standards for more general charities.
I'm not naming any of those groups because there's a potential catch: How reputable is the group that rates other people's reputations? And I don't want to recommend someone without knowing. Years ago I came across a news story about an organization that rated colleges, and that had given one particular college their top rating. But, the news story said, investigators found that that one college was the ONLY college they ever gave a rating to, and that their address was the same as the college's address. It turned out, of course, that the college was a scam.
The other method is to take some time to investigate the charity.
For starters, get a copy of their annual report or their newsletter. If they're total frauds, often they don't have an annual report or a newsletter. Of course a fraud could make up beautiful flyers describing all the wonderful work they do, with pictures of people they helped and detailed case histories, and it's all complete fiction. But that's more work than most con men go to. I've gotten lots of pleas for contributions from people who call on the phone or come to my door or send an email. If the message does not have a logo, a mailing address and phone number, reasonably coherent English, and a fair amount of text describing what they do, I don't give them anything. They COULD be a new start up that hasn't had time to prepare these things. They COULD believe that pretty flyers are a waste of money and they want to put all their resources into helping the needy. But more likely it's a scam that somebody through together in his basement.
Of course the best thing is if you personally know people who are officers in the organization. (Well, assuming you personally know them AND you know that they are honest people. If you know the president and you know he's a sleazy con man, you might want to stay away from that group.)
See if you can find information about the charity in the news or on-line. If they're being investigated for fraud by the Justice Department, you might want to avoid them. Etc.
Maybe you've thought this through, but you also might want to think about exactly who in Greece you want to help, and what your philosophy of charity is. Do you want to help people who lost their jobs because of the economic problems there and who are now unemployed? Do you want to donate to the government to help them balance the budget? Do you want to help support an orphanage or a homeless shelter, or give money directly to needy people? Etc.
And one piece of unsolicited advice: Unless you have millions to give -- and I'm assuming you don't as you said your first gift would be $50 -- I'd pick one or two charities and give regularly to them. I think you can do more good by giving $X per month to a single charity than to give to a different charity every month. You make more difference.