I'm very new to keeping fish as pets. I was surprised to find out that you can order fish online and have them shipped. Is there any way to be sure that the fish will be healthy? Should I just stick to local stores?
There's nothing inherently sketchy about ordering fish online: most legit dealers (whether individual breeders or larger fish farms) should know how to ship fish safely, and I've seen many who are confident enough to offer live-on-arrival guarantees. Most dealers will describe how they ship pretty clearly, and you should be able to get a sense of how legit they are from that: Good bags, some sort of temperature control depending on the weather (heat packs, ice packs, etc.), and fast shipping are all things to look for. If you get the sense the dealer doesn't really know how to get the animal to you, or is being cagey about how they'll do it, I'd probably say look elsewhere.
The health of an online dealer's stock can be a gamble, but the same can really be said for the ones at your LFS -- it's true you can avoid any obviously bad fish you can see in person, but a good dealer won't sell you an obviously sick/dying animal regardless of whether you're there in person; and even healthy fish can have latent diseases and parasites that are brought out by the stresses of being transported to your home.
So there's an element of trust with any new dealer that you're considering. See what kind of reputation they have on the various aquarist forums, ask anyone you might know who's done business with them, even get in touch with them and see how they answer your questions. Then, if the price is right and you're convinced enough to give them a shot, go for it. If you can, quarantine is always a good idea, since it mitigates a lot of the risk in bringing home new animals.
Personally I tend to get my fish from a little local store, because I like the owner and he usually has a interesting and healthy (thought small) selection. But I'm planning on adding a few dwarf cichlids in a few months, and I'm probably going to get them from a specialty cichlid farm that I've heard good things about: they're just the next state over, but overnight shipping will probably cost less then the gas it would take to drive there. We have some of the big-name pet stores around here too, and while I've never had outright bad luck with them, I think I trust the specialists more, whether online or brick-and-mortar.
It's not a bad idea; there are pros and cons to both.
In the store, you get to see the fish you're sold, and make sure they're healthy before taking them home. Online, you might not get to see the fish firsthand, but you can get fish directly from specialty breeders; fish that local stores might not have the setups to care for.
As far as shipping goes, most will ship it in breathable plastic bags, to ensure that the bags don't run out of oxygen. I know several that add more oxygen to the bag to help as well.
Personally, since shipping is so high, I would check with the local stores for fish first. They might even be able to order some for you. Otherwise, just make sure you order from someone with a reputation for selling good quality fish.
Both have their pros and cons.
I would personally get them from a store as I know the travel time they have been in the bag for, your oxygen levels would be fine. Also any problems with them I can get a quick response.