My active interest really started in 2015 when Z-Man republished Traders of Carthage as Traders of Osaka, and I played the hell out of it. There were a couple games getting US distribution through AEG and Grail Games. When the BGG Store started carrying imports, I took a chance on King of Frontier and Minerva (based on positive reviews from opinionatedgamers contributors like Joe Huber and Lorna) and that’s what got me into importing games.
Different games have required different amounts of legwork to acquire:
Traders of Osaka, Trains, Too Many Cinderellas - Bought the English versions
The King of Frontier, Minerva, Wind the Film! - Purchased from the BGG store
Yokohama, ButaBabel - Amazon.co.jp ships international.
Neos - subscribed to the Neos forum on BGG and posted in a group-buy thread as soon as it popped up
Age of Craft - Received a Geekmail from someone local who had a copy and worked out a price, because I had it marked “want in trade” on BGG
Familiar’s Trouble - Sent a DM to US importer Ninja Star on twitter, after spotting copies in a picture of their convention booth
Tricks & Deserts, Pecunia - By far the biggest pain in the butt, set up an account with a JP-based forwarding service and purchased from a small Japanese online store that wouldn’t ship internationally
Actually tracking down copies of these games is definitely part of the appeal. I have one more TGM 2017 game on the way, in fact.