Generally, anywhere from about $30 to about $150 depending on your location and size of the fish. Personally I opt out when it comes to shipping fish because its just a pain. But if you LPS doesn't have that certain fish, or no one in the state has that fish, the only other option is by mail.
Ok I shipped a fish personally just a few months ago.
Depending on quarantine and state shipping, it changes a bit. For myself with absolutely no state issues to send 1 fish it cost $35 USD. I shipped 1 fish, weighed 2kilos, 30cmx20cmx20cm I think were the dimensions. Because I couldn't get a cooler box, I just had a fish in a bag, wrapped in lots of shopping bags for safety (if the bag broke, would stay contained, for insulation and cushioning) then in a A4 paperbox packed in tight with newspaper. If you could get a smaller styrofoam cooler box you could probably manage smaller packaging, but it likely won't cost you less as they usually charge in groupings, like items between this size/weight is $30, items between this size/weight is $50 and so on. Was a short distance, so I just got standard shipping. The longer the distance, the higher priority you'll need to pay for. Airmail was $30usd extra I think...and that's because I asked for "special fragile treatment".
Then also depending on how its being shipped... by aeroplane will cost you extra, unless it's linked to someone flying (eg you're flying somewhere and take a fish as "baggage" it's usually free baggage with just the pet transport fee of about $30-$50, or $100 for a big box of fishies like the LFS do).
If you have a nice LFS, try go in and chat with the store manager. I found them very helpful. You can ask them who they use for transporting their fish. And if you're shipping a lot of fish some LFS's will give away their boxes free. If not, try supermarkets with fish sections (I mean edible fish) and fish sellers the type that are importing and exporting fish. They often either give them away free, or sell them for $5-$10 a tub (depends on size). We have lots of companies ith fishing vessels attached that sell their excess styrofoam cooler boxes to petstores and anyone interested.