Though flies are pretty common in real life, in Animal Crossing: New Horizons, they're blissfully rare. The fly is one of 80 bugs you can catch in the game, and while it's not worth much, you have to put some effort in if you want to catch a fly and fill in your museum and Critterpedia. The good news is that flies appear year-round and at any time of day. But oddly enough, the first thing you need to do to catch a fly... is go fishing.
A fly in Animal Crossing: New Horizons' Critterpedia.
Fish until you catch garbage (a can, tire, or boot)Drop the garbage somewhere outsideWalk around the island until a fly spawns around the garbagePull out your net and catch the fly!You can also use spoiled turnips to attract a fly (instead of garbage) just like you can do with ants. However, because spoiled turnips are the only way to attract ants--and ants seem to be more common than flies--you'll likely have to endure a lot of ants before you can find a fly. Using spoiled turnips also costs bells (both when you buy the turnips and then fail to sell them at a profit), whereas garbage only costs a little fishing time. Either way works, though!
Like with many bugs, you should only try to catch a fly when it's not raining. Keep in mind that it can take some time for a fly to appear, so just be patient. The type of garbage you use doesn't seem to affect whether a fly will spawn, but it has to be raw garbage, not anything crafted from cans, boots, or tires.
Nook's Cranny price: 60 bells eachFlick price: 90 bells each