There are a few ways to find artifacts:
- Artifact spots (the little worm-like things in the ground that you dig up with your hoe)
- Fishing treasure chests
- Artifact troves, which you can get by trading 5 omni geodes to the desert trader
- Some enemy drops (e.g. duggies can drop chewing sticks)
- Some artifacts can be found by hoeing dirt in the mines
Also, as I'm sure you know, breaking geodes at Clint's gives you minerals, which are not quite the same as artifacts but can also be donated to the museum
That being said, most artifacts only show up in a few of those - e.g. glass shards can only be gotten from artifact spots at the beach and from fishing. You can check your collections tab to see which artifacts and minerals you're missing, and compare them to
https://stardewvalleywiki.com/Collections to see where to get the ones you're missing.