A lot of being patient, mostly. I've been actively collecting these for more than 5 years, although it's been recently that I've gotten the shelves and started displaying them. To give you an idea, I had all the Game Boy Pocket colors except for green for quite a while. The day I walked into Half-Price Books and saw it there with the $15 price tag was a great one. Another is knowing what real serial numbers and models look like, then looking for incorrect listings on things like eBay. My extreme green Pocket was only about $10 (and free shipping!), and it was listed as "Transparent Yellow." I knew immediately which model it was and was the only one that bid on it.
I do hit up garage sales when I can, and I have parents who are retired and go garage sale-ing about every week. They call me when they find game stuff and they've landed me a couple. I also never drive by a Goodwill or Volunteers of America without stopping, just on the off-chance. My platinum GBA came from a Goodwill during a deal on everything in the store, so it and a couple games cost me $5. One of the first items we got was our Nomad, which we got from a flea market when the guy swore it didn't work. Ronalopolis asked what they'd take for it, he said $5 since it was broken, and we took it home, just to find that the adapter plug was a bit loose and that the contrast was turned completely to one side.
Another tip would actually be to check out the local used game stores. The one in my town doesn't price Game Boys any differently based on color, so even though the ice blue Pocket would usually be a bit pricier, they had it listed at $15 along with all the other Pockets. The manager at another game store near us has gotten to know us and knows what we collect, so when we walked in he immediately showed me to those two Pokemon Game Boy Colors. He had $35 each on them but after we'd grabbed another big item (the Ace Combat 6 flight stick) he knew he could get me for another $40 for selling them for $20 each and have a nice big sale at once.
I guess it really comes down to just keeping an eye out for what you want. Most of our handhelds felt like steals, but it's because I've put the time into researching the models, knowing their value, and I've just kept making it a point to be always looking, no matter where you go. I don't know how many weekend getaway trips have yielded old games, just because we've used Yelp to find local thrift stores on our way.