The process depends on whether or not you will be flying with the dog. If you are flying with the dog, it is simpler and cheaper. The country also matters a bit, as not all countries have international flights that can carry animals(and not all airlines do private consults, some require a shipping company).
Since the puppy would be too young for a rabies vaccine, the process is quite simple, health requirement-wise. In order to enter the USA, the puppy would just need a health certificate dated within 10 days of arrival in the states, that basically says "yes this puppy identified by this microchip _______ is in good health". Regardless of flight option, a health certificate with permanent identification is required.
If flying in cabin, check with the airline for dimensions. They vary a bit, but generally must be less than 7 inches wide and 10 inches tall. Material doesn't matter, but it must contain any mess the pet may make.
Cargo pets must have a plastic or metal crate with ventilation on all sides(but must not be able to "stick out" any limbs), must be secured with metal nuts and bolts, have both food and water bowls accessible from the outside, have LIVE ANIMAL stickers with directional arrows on all sides and must have absorbent bedding of some kind(but not straw or shavings). The animals records should also be attached to the crate, along with basic information and contact numbers.
The best way would be to fly over and carry on the little one. I flew with my standard from Sweden to Germany as a carry on at 8 weeks, so a moyen shouldn't be an issue for size. This will likely be your least expensive option. However, not all airlines allow in cabin pets for international flights. In May 2013, my cat was $140 as a carry on.
Your other option, if you are flying with the puppy, is to ship them as checked baggage. This is the next least expensive option and usually flat-rate, regardless of size. In May of 2013, my 40 pound dog in a 36" crate was $300 on my flight.
If you cannot fly to pick up the puppy in person, your pup will fly as cargo. This is priced by weight and occasionally size as well. Most airlines list their cargo shipping costs online. I was quoted $650 to get my cat from Baltimore to Germany thru United in October 2013.
Depending on the airline's policies, your pet might have to fly as cargo and must be booked thru a shipping company. This is the most expensive option. I have been quoted almost $1,300 to get a cat from Baltimore to Germany.
So, as you can see, the cost and exact process can vary greatly depending on country of origin, airline and even time of year(heat and cold embargos means you might only be able to ship a puppy in the spring and fall).