Sad, but true - the most important thing you need to know when buying vintage Western Wear is: you need to be patient, and you need to be ready to bid farewell to your hard-earned dollars.
Know your Western Wear style
Western wear, just like any other type of clothing, evolved throughout the years and often took on the characteristics popular in each era, so familiarising yourself with a bit of history would be my first tip.
1800s-1900s - those OG pieces (if you happen to have 'em, I tip my hat!), were made out of practicality first, so you'll find durable fabrics like denim, canvas, wool, cotton and calico.
1920s-50s - the mass migration out West, the popularity of rodeos, the cowboy image romanticised in films in music - these were the heydays of Wester style, so the clothing became much bolder, with plenty of embroidery and chain stitched motives. Still, though, the fabrics were mostly natural, e.g. wool gabardine, mother pearl snaps, cotton, and silk. Broad shoulders, cinched waist and straight-legged pants were typical.
1960s-70s - the hippie movement in the 60s brought a bohemian twist to Western wear, so other than a more relaxed fit, we have fringed vests, flared jeans, and turquoise jewellery. In the 70s and towards the 80s, with mass production was at its finest, synthetic fabrics were introduced. Typical from the era are permanently pressed shirts and pants and lots of denim.

Set alerts on marketplace platforms and search them daily
If you're serious about some particular piece or brand but struggle to find it on eBay or Etsy, do not lose hope, pardner! And I'm not saying that just because, but this is a method that worked for me multiple times.
You can save your search tags on eBay and revisit them daily; make sure to set the 'worldwide' location filter. Although there's no such feature on Etsy, the best thing to do is create your favourite board with the styles or brands you're after - Etsy's algorithm will suggest similar items in their 'because you viewed' tab.
And if you're shopping on independent reseller's websites, or like a particular shop's selection, add them on socials and sign up to their newsletters to always know what and when they're dropping.

Check out auctions and bidding sites
Usually, the big items like Nudie’s suits or those extremely rare late 1800s pieces will sell via auction houses. Some specialise in Western memorabilia, while others might have a broader focus. Do your research to find the ones that regularly feature the kind of items you're after. LiveAuctioneers is one of my favourite place to go, but I’ve seen numerous vintage western items going on sale even in London’s sites, so my tip again would be to sign up to newsletters of such places to be notified whenever they’re planning on the bid.
Be wary of reproductions
The more details on a Western shirt or a blazer, the harder it is to replicate it, but especially when it comes to more recent pieces, the market is flooded with repros. What I notoriously see are leather and suede vests, jackets or chaps, mass-produced in India or Pakistan, pretending to be Native-made. Some of the listings would even have a vintage image as a header or an image stolen from a small manufacturer, but when you study the description, the price and the shipping time, you can easily spot that it is not a legit item.
And don't get me wrong, I have nothing against those companies, they too have to make a living, but stealing the images and misleading with the origin - that is not very rootin' tootin' of them.
Don't wait too long
Nothing haunts us like the vintage we didn't buy, so if you see something you like and it's a sought-after piece, just hit that 'buy now' button. Worst case scenario, if the seller doesn't accept returns (always check the shop policies), you'll sell it on eBay.
But if you're not a 'fuck it' type of a cowperson and you want to make sure that you're getting something that you can truly enjoy, then:
a) invest in a measuring tape and compare the item's measurements with something that you already have and fits you right, so shirt with shirt, low-rise pants with low-rise pants etc.
b) ask questions - send the DM, and fill out the 'contact us' form. Many small businesses will even reserve or keep the item on hold for you if you ask nicely. In general, y'all, don't be afraid to ask anything ever.
Choose reputable resellers and stores
Scammers don't sleep, so before you decide to PayPal somebody half of your monthly spending allowance, check if they have any reviews, if they're active on socials, if they're registered company or if you have any buyer protection above you. With big platforms like eBay or Etsy, there's always customer service, but I'd avoid blindly relying on it and try to avoid any unpleasantness.
Bonus tip: my favourite online western wear resellers
If you've made it this far, you're a serious player. Below, some of my favourite vintage shops that always have some good vintage Western Wear in stock (apart from my very own, Vintage Cowboy Store):