By testing every minor change as I go in the major browser engines. That means webkit, blink, quantum, edge, and trident. Then for major changes / milestones I test across different OS in as many combinations as I can.
To that end whilst I may do my primary work on Windows 10, I have VM's of older Windows versions, different linux distros, and OSX set up under virtualBox so I can test for differences.
It's often surprising how often Firefox for Mac doesn't behave like FF under windows/linux does, or how certain webfonts are illegible crap on different OS font renderers... or how different fonts and font renderers can result in the same declared size fitting wildly different numbers of characters per line.
MOST of them are free, for older stuff like legacy Windows it's not that hard to find an old abandoned/discarded laptop with a valid product key.
The one that is the hardest fight is Safari, given that on mobile old versions are still in common use, and to be frank webkit is aging like milk even on desktop. Ever since Google absconded with all the actual talent to fork off blink, webkit has been rotting on the vine with no real efforts to even TRY to keep up to other browsers.
There's a reason a LOT of dev's are now calling Safari "The new Internet Explorer". We're stuck supporting old versions with the stupid browser prefix trash for both desktop and mobile as other browsers -- even Edge -- leaves it in the dust on performance, standards compliance and just plain usability -- but in the mobile space failing to support it fully/properly is as big a suicide as not supporting MSIE fifteen years ago would have been.
Particularly with crApple's vendor lock-in policy in regards to competing programs in their stupid "store". Could you imagine the public reaction if M$ pulled that stunt on the desktop -- they got in trouble for offering IE for free... but blocking competitors from even being installed/offered? But no, it's the almighty Apple so we all have to get down on our knees and...