Start by visiting the organization's website. Here are the four I currently sponsor with:
Compassion: Compassion International is awesome! Currently, sponsorships are $38/mo. You can also send extra money for birthdays, Christmas, or family gifts. Compassion also offers periodic trips, in which you could visit your sponsored child (which would be awesome!).World Vision: Sponsorships are $35/mo. WV makes letter writing very easy by sending cute little crafty things that you personalize and send to your child.
Kenya Kids in Need: This started as a Yahoo group who decided to come alongside an amazing man in Kenya, who started a school for kids who were too poor to go to Kenya's "free" schools (Even for "free" schools, kids were required to get uniforms, school supplies, etc.). We have grown tremendously in the last few years. One very wonderful feature of KKIN is the "online store"--You can order gifts (clothing, blankets, school supplies, and more) for your sponsored child, and they will be purchased right there in Kenya, thereby helping the local economy as well.
Children Incorporated: God recently put U.S. kids on my heart, and so I started sponsoring with CI. You can choose from Appalachian, inner city, and Native American. They also have overseas sponsorships. Sponsorship is $28/mo, again with the option to send more for birthdays and such. WIth U.S. kids, you can also send packages, and know that they will get there!
There has been a lot of talk on the web lately regarding the importance of our letters to our sponsored kids. Letter-writing can be tough! The organizations will tell you to "avoid discussing your material possessions." It's amazing, even though I think or myself as a relatively non-material girl, how much of my family "news" involves things: "I got a Droid phone; it's like a little hand-held computer!" "My car just turned 15 years old. I wonder how long it will last... "
I have not always been the greatest at letter-writing to my kids. But after reading some excellent blogs on the topic, I am all fired up about it! Check out my new favorite blog for letter-writing suggestions and lots of heartfelt testimony about sponsorship in general!
As for the financial end of things, this can be very humbling. Ritu from Bangladesh is our best letter writer. We send her some extra money for her birthday each year. The first year, we got a letter explaining that she used her birthday money for a blanket for her mother ("because she didn't have one") and a goat for her family. My kids, who really wanted some new game-playing gadget at the time, were pretty silent after reading that letter.