First, get a character that uses Claymore like Noelle, Razor, Beidou, etc, since Claymores can destroy ores and crystals easier.
Second, depends on what kind of ores and crystals you wanted, you need to explore the map. Go to mountain areas like Stormterror’s Lair or Stormbearer’s Point to farm White Ores and Crystal Chunks. You can also use this guide to check other spots.
Third, if you have Ningguang, make sure you place her in your active party, since she got a passive skills that can detect nearby ores (it’ll be shown in your mini–map)
Lastly, use the Dispatch feature, since there are some dispatches that will give you ores (you need either 12–20 hours toget White Ores and Crystal Chunks).