Reading the listing. Look at the title, the gallery picture, the price, location and accepted payment methods. If anything there looks shaky, go back. Keep in mind that on eBay, another one will be listed again soon. If all is well, go on to the description and the rest of the photos. If there's only one photo, especially if it's dark or out of focus, check to see if the seller invites you to ask for more pix. If not, nature leads one to suspect something is being hidden. That may not be true, but it's pretty easy to take good pix, even with an inexpensive digital camera.
If the description includes damage, like dents or bent keys, be sure to see a good close-up of it. What one person describes as "minor" may not be what you consider it to be. You also want to know the serial number of the instrument, or at least the first digits of it. Some sellers don't list serial numbers because unscrupulous people have been known to make false reports of stolen goods based on the numbers, but the first several numbers help date the instrument and should not be refused if requested through ASQ.
Which brings us to: Ask, ask, ask. If a seller doesn't care to answer your questions before you bid, how helpful will he be if there's a problem afterward?
Many of the sellers whose listings say something like, "I don't play this, so I can't tell you whether it's playable." If someone's clearing out Grandpa's attic and finds and old flugelhorn to sell, that's one thing. But if the seller is listing ten flugelhorns from different makers, expect better. It doesn't cost an arm and a leg to take an instrument to a technician and have him evaluate it. Expect that any seller who lists several instruments either to have a tech on retainer or make some other effort to demonstrate proof that the instrument is in the condition described. If the seller says the horn has been cleaned, adjusted and play-tested, so much the better.
If you see a brand-new instrument selling for half or less of your research prices, beware. There are two main possibilities: That the instrument is a shoddy, usually foreign-made, copy of what you want; or that the instrument doesn't really exist and is listed by a scammer. Don't even open those listings, because of the phishing that's been going on all over eBay. High-dollar items like musical instruments are especially vulnerable to this.
Compare shipping costs among items, too. If the instrument is being sold as-is, with no returns accepted, you may end up stuck with something you can't use. If the seller accepts returns within a limited time, be sure you adhere to it.
Bidding: Once you've found your item, bid mindfully. Decide how much you are willing to pay, wait as late in the auction as you can stand to (the last five minutes is good) and then place your maximum bid. This isn't the only bidding strategy out there, but it keeps one from getting into a bidding frenzy and spending way more than one can afford because of an overdose of adrenaline.
Once it gets to you: Okay, you bid, you won, you paid. In most cases you'll need to be home when the item comes or make arrangements to pick it up from the shipper because you'll have to sign for it unless you got a very inexpensive deal. Look the parcel over very carefully before you open it, preferably in front of the deliver person. If the box shows significant damage, you want it to be noted immediately. Open it and inspect it for obvious shipping damage. If it's been rattling around loose in a box for a thousand miles (or even less), even an instrument in its own fitted case can be damaged beyond repair. If all seems well,
Have it evaluated: At this point, you need some outside assistance. Within the time-frame of the return policy you need to have an experienced person check the instrument out thoroughly, even if it's brand new. Your child's teacher is a good start - although teachers have very little time in class to give the instrument a full inspection. Your local music store can help you better, but if they have a backlog for their technician they may not be able to do it in time.
Most instruments, even new from the factory, need some minor adjusting after shipping. You shouldn't consider spending a few dollars on a tune up a matter to take up with the seller, but if the horn is significantly not as described, you need to contact the seller and follow all the procedures given elsewhere on eBay.
Success: Once you've received your purchase and made sure you got what you paid for, your child is on his way to a lifetime of enjoying music.