Normally when buying a bird online, you will pay using something like paypal, and if they need to be shipped, that will be done at the purchaser's(you) expense. You will also be responsible for promptly picking the birds up at the airport. Some people will want you to pay for their gas to drive to the airport as well, which is reasonable considering how expensive gas is and that some people may live well over an hour from the nearest airport that allows animal shipping. I'd be very wary, $125 for a breeding pair of sun conures is very cheap, I would be afraid that it is a scam altogether(meaning there are no birds) or that they are a pair that doesn't produce anymore or for other reasons do not make good breeders. Unfortunately, this is really only something you can know by chance, and that's where it helps to go to a trusted, reliable breeder, it also insures that you are getting an unrelated pair. I know I probably sound like a bit of a hypocrite because of the way we got our amazons, but honestly, I'm not even 100% sure if they are a male and a female, I was told they were but wasn't given any proof, we bought them more to give them a good home that they desperately needed and we were just going to take any babies we may get as a happy bonus. Even if they never produce, we will still love them and care for them the same
I also noticed that they only other listings the seller has is for "rare geodes" which seems kind of fishy. I would recommend talking to them via email and phone. Do your research, ask for multiple pictures and make sure that you can't find those same pictures listed somewhere else(google image search is good for this, but sometimes that's not enough). Ask a lot of questions and try asking the same questions, worded a little differently and make sure you get the same answers. It may also help to call back later from a different phone and act like an entirely different person. If you call once and act like a caring bird owner you may get a response that makes the seller sound like she took really good care of these birds, if you call again and sound like you are what I will call an "unethical breeder", and they give you different answers to the same questions, it's pretty obvious that the seller is just trying to tell you what you want to hear. I hope that makes sense, I know the last part seems kind of deceitful but when in a situation where you don't know the seller, cannot meet them in person and can't get any references, you have to do what you have to do to protect yourself. Otherwise, go to a good reputable breeder, most of the time you really do get what you pay for.
Forget to clarify on the payment details, you will have to pay for the birds and shipping before the seller will ship the bird. You can pay using paypal or a money order(I wouldn't suggest using a credit card directly, and you never send cash or a personal check to someone you don't know). Once the seller receives payment they will set up an arrangement to ship the birds which will depend on both of your schedules and the weather.