There is no way to answer this question other than to say that it will cost quite a lot of money.
Any airline that flies dogs and cats can set their own fees for providing that service. The airline can also set its own rules about the maximum size/weight of dog that they permit in the cabin (if they permit that at all). If your puppy is too large/heavy – the it must go as cargo.

Are you going to fly on the same planes as the puppy, or will the puppy be sent as unaccompanied cargo? That makes a difference as well.

You need to go to any of the dozens of travel sites on the internet and enter the departure airport (where ever you or the dog will start from), and the arrival airport in California and some dates. Whatever flights show up will tell you which airlines offer service between those two points.

It may also be very useful to pick flights between your Russian or Ukrainian departure point to some intermediate destination, like London, Paris, Amsterdam and so on, then find flights from that intermediate city to your CA destination. That may give you a larger range of choices of airlines

This will certainly end up being a multi-stop flight, with several connections, quite possibly on different airlines. That makes pet transport much more difficult. If you pet is traveling as cargo, then you end up having to rely on the airline personnel to take care of the puppy – provide food, water and deal with waste. They also have to be sure to get the puppy from one connecting flight to another. Depending on schedules (and especially weather at the moment), there may be 12 or more hours between planes. Where does your dog go during that time?

With long layovers, there may be issues with health requirements for the countries in which the layovers occur. You need to find out about that.

You certainly need to look into the requirements for importing a dog into the US. Start here:
http://www.aphis.usda.gov/import_export/animals/animal_import/animal_imports_pets.shtml

When you think you have a possible route worked out on one or more airlines, then you MUST call each airline and find out:
1) Do they transport dogs
2) How much will it cost for the flights involved
3) What health certificates and information do they require in order to permit your pet on board. Note that this requirement is different from the US import requirements.
4) How are connecting flights handled
5) What happens if a flight is delayed
6) What happens if you miss the connecting flight, or it is canceled
7) What about food, water and waste

You must ask those question of _every_ different airline involved in the whole journey. The information you get from one may not apply at all to the next.

You have tons of work to do in order to accomplish this.

Or – you could hire a professional pet transport company to handle all of the details for you – at many times the cost that the airlines would charge you.

Be aware that a trip like this will < > be a kind thing to do to a puppy. They may end up staying for at least 24 hours in a cage – probably away from you – handled and looked after by total strangers – in a situation and environment that it cannot _ever_ understand.

Also be aware that pets do die sometimes while being flown form place to place.

Think _very carefully_ if you want to make that puppy go through the trauma that such a trip will require.

I was traveling with my puppy form Moscow to L-A about 4 years ago (by Aeroflot) and it cost me about $340. I do not know how much it is now. I would recommend to call Airlines you decide to use and find that out, I think prices vary for each airline and size (weight) of your pet.