This is a darned simple Instructable that might help you avoid a few wrinkles or creases on your next flight.
I travel a good bit, and on airplanes I'm often seated in "Coach," which I believe they used to call "Steerage," but I digress. Since most of my travel is business travel, I'm usually wearing a sport coat. This method has avoided some wrinkes for me in the past.
Side tip: sometimes even when I'm not traveling on business, I'll wear a sport jacket. Consciously or not, people tend to treat you better when you're better dressed. I don't know why, but when I take the same face (and facial hair) through security or to a rental car desk in a t-shirt and jeans, I get a noticibly different level of service than when the same face attired in a manner many would call "more respectable."
Step 1: Before You Leave, Equip Yourself.
Obtain the hook, and keep it handy. Clip it to a carry-on item like the zipper of your laptop bag, or your keys, or just keep it in the jacket itself. Note: A full-size caribiner is too thick for this purpose, get the cheap, little ones.
I grabbed a bunch of these faux caribiners at the keychain section of my local hardware store. Don't pay more than 50 cents for one of these cheap little clips, though, and don't try to support more than a couple of pounds on them either.
(Coins are shown for size comparison purposes.)
Step 2: Use Common Sense.
The easiest way to hang a jacket while on an airplane is to politely ask a flight attendant if they could hang it up for you. If you get them when they're not busy, they're usually glad to oblige.
If, on the other hand, you're like me, and your jacket pockets are loaded with iPod, phone, chewing gum, boarding passes, and the occasional passport or other handy/important stuff, you may not want to let the jacket out of your sight. If so, read on...
Step 3: Assess Your Seating Area.
Look at the tray table on the back of the seat in front of you:
If you're lucky, you're on one of the planes that's been outfitted with a hook already built into the catch that holds the tray shut. You don't need this Instructable. Hang your jacket, and bask in the satisfaction. It's ok, go ahead, really.
If you're seated behind a bulkhead and not another seat, see step #2. If that fails for some reason, the other option is to fold your jacket carefully, and place it gently in the overhead bin. Then avert your gaze when the couple with three shopping bags of souvenirs "reorganizes" someone's rollerbag on top of your jacket to make room for their family-set of matching embroidered sombreros.
First, simply clip the fake 'biner onto your jacket. Usually there's a good strong loop or well-sewn label at the top.
Step 4: Insert the Fake 'biner... and Hang It!
1. Turn the tray table latch to the open position.
2. Insert the caribiner clip into the gap between the table and the seat.
3. Turn the latch on the tray table downward so that it sits within the caribiner. The latch secures the clip, and the clip secures the jacket.
"Walla, the trick, she is done!" Now go ahead and ask for extra peanuts to celebrate.
Step 5: Afterthoughts
If you need the tray in the "down" position, this method won't work that well on its own. Instead, bend a large paper clip around the latch, and hang the fake caribiner from that, with the jacket hanging between the tray and the seat.
You can, of course, use this method to secure other items as well. I've had success attaching my iPod case to the seat in front of me using this same method. The screen winds up at eye level.
Use your imagination, but don't overload the clip. Remember they're cheap little pieces of aluminum that are meant to look stronger than they really are.