How does one get rid of sinus congestion without resorting to drugs?
IANAD, etc.
Try horseradish, jalapeño peppers or foods with capsaicin. Workers in horseradish processing plants report little or no sinus congestion ever (as seen on 60 Minutes some years ago).
Lots of people around these here boards use these disgusting, but apparently effective, nasal pot devices (damned if I can remember what they’re called). They pour water into their sinuses and the world is right again. Seriously. Someone will be along with the straight dope on these things. They sound like a horror movie to me, but everyone whose tried it sings its praises.
A Neti Pot. They are very effective, at least for me and I am known for my use of nasal spray.
To keep my sinuses in line, I take 1 tbsp of LOCAL honey. Take once a day during allergy season, then cut back to once a week during off season. Unfortunately, I havent found any local bee farms in this area - yet (recently moved). Until then, I’m doing the OTC meds since peppers will tear my stomach apart.
I had a bacterial sinus infection a while ago, which I grumbled about in this disgusting thread: My sputum stinks! My phelgm reeks! My mucus is mouldy! (TMI, if you hadn’t noticed) . In addition to the anti-biotics, the doc told me to get a saline spray over the counter from the pharmacy, to get some relief until the anti-biotics kicked in. It seemed to help considerably.
That’s IT! It’s something of a cult classic around here. Fortunately I don’t have sinus problems and rarely even get a head cold, so I’ll just have to believe it’s all that and a bag o’ chips.
I’ve used the NeilMed in the past with some favorable results. Same idea, but different mode of getting the water into your nose. It feels kind of funky the first few times you use it, but you get used to it, and it does feel like it washes a lot of crap out.
That is a chemical. 
Get in the shower and turn it on as hot as you can stand and just let it run. I’ve always found the steam to be excellent for the sinuses.
I’ve become a fan of the OTC saline nasal sprays. Same general idea as that NetiPot as far as I can tell, but premixed and ready to squirt.
Nonsensical Cures for Sinus Congestion
-Crouch on all fours and bark like a tree?
-Cover your face in school mucilage and unwashed socks?
-Stand in a strong wind or electric fan and yell, “I condemn thee, Imp of the Sinuses!” three times?
Drinking warm beverages (unless you are concerned about the dihydrogen oxide 
). Also, if it’s allergy related, avoiding the allergen.
Yes, and not just from eating those things. Open up a jar of prepared horseradish (not horseradish sauce,) and take a deep sniff of the vapors in each nostril. Sauté some hot peppers, or add hot sauce to vegetables as you sauté them. You’ll notice a dramatic effect.
Search the boards for “neti” and you’ll get many previous discussions of nasal irrigation.
I haven’t yet worked up the courage to try the neti pot, but I get a lot of relief from sterile salt water drops from the pharmacy. Basically the same idea, but in smaller, neater packages
There are two things to remember: [ol]
[li]the water will flow downhill, so keep the place where you want it to flow towards as low as possible, and put the drops into the upper nostril; and[/li][li]breathe through your mouth![/li][/ol]
There’s a spot under you eye that you can push down on, right on the edge of the eye socket, that somehow clears the sinuses if they are not too badly congested. Someone taught me this long ago and told me that it cuts off a blood vessel to the sinuses, which reduces swelling in the wall of the sinus and thus enables the stuff to flow more freely. Or it’s psychosomatic. YMMV.
Anyway, I found a tutorial online which features these spots plus other pressure points: here