Traveling with Yorkies - click on that to get to teh right place.
I have flown internationally with Meg and I will tell you that if you want to take your pup with you, it's 1) completely doable, and 2) totally important that you choose the right airline. Different airlines charge different amounts of money. For example, United costs $220 (international) one-way, but Delta costs $550 (international) one-way. Do your homework ahead of time by going to the airline's website, clicking on the travel questions/baggage section, then looking for anything that says "pets" or "special baggage". Some airlines will not allow dogs in the cabin at all, so if you want to take your baby, start researching your options now.
Another important thing if you want to fly with your pet is that you MUST make a reservation for your pet ahead of time if you want him/her to travel in the cabin with you. I HIGHLY recommend that you do not allow him to travel in the baggage area - for safety's sake. However, FAA regulations allow only a certain number of dogs in teh cabin for flights... usually 2-3 dogs are allowed in economy class, depending on the size of the airplane. Once those spots are filled, you can't get your dog on the plane (unless s/he is a service dog). If you are buying your ticket on expedia or something, call the airline first and ask if they still have room available for in-cabin dogs on the flight. Then buy the ticket online and call the airline back asap to reserve your dog's space. If you go through a travel agent, they will do this work for you.
Then you'll need to purchase an airline-approved (well-ventilated, waterproof bottom, and within size regulations) carrier. I have a soft-sided Bergan Comfort Carrier and I love it. (So does Meg!) Get your dog used to the carrier ahead of time by leaving it open on the floor and letting your dog explore it. Put a favorite toy or treat inside to help them warm up to it. Don't zip them up until they've had some time to get used to it.
Bring along a leash, water bowls, a toy or two (although Meg never plays with toys in her carrier), food, etc. I bring NutriCal with a vet prescription sticker on it, just in case. If your dog is paper trained, you're in luck. Take the dog to the airplane bathroom (with baby changing table), put the pee pad on the changing table, and you're good to go.
You will need a health certificate issued within 10 days of travel (the airline will need this, and customs might need it in Lithuania). Look into which vaccinations are mandatory. Based on the link bchgirl posted, it looks like your dog will just need the Rabies vaccination, but it needs to be given MORE THAN 30 days before you get on the plane. You will also need to have your dog microchipped/tattooed according to that website. Again, do your research and make sure that the website you are reading off of is a legititate, official government site.
If you have more questions, feel free to PM me. Also definately read through the Traveling with Yorkies section. THere is a lot of great information there. Good luck!