Same way you get gold. It's just a little less common. I still wind up with tons of it.

Sandstone outcrops

Different outcrops drop different Items, Sandstone one's are everywhere except safe shallows

Also a bucket load of silver, gold and diamond on one of the islands.

Wiki

You can find it in sandstone outcrops

Only in [BZ]

And copper, too.

They say you can also find chopper

Find the border between the grassy plateaus and the kelp forest and on the border(the kelp forest is kinda taller so youll see like a elevated area then a drop into the grassy plateaus) youll see tons of outcrops of sandstone

On those weirdly shaped platforms in the grassy plateaus youll see sandstone outcrops on the side of it

Sandstone can contain gold,silver or lead, each one have a about 33% chance of dropping ,so you wont allways get silver, but lead and gold is very useful

Btw, limestone outcrops look like very rough rocks that a pretty wide, and they contain titanium and copper, while sandstone ones look like neat little balls of stone and the drop silver gold and lead

Silver will spawn with cobalt or gold, iirc. If you find cobalt or gold, silver might be nearby, though you are also likely to find gold + iron or cobalt + iron + nickel + silicon

Just keep searching using a Large Grid Ore Detector, looking for "ore spots". You can find them under ice, like in the image, but also under normal terrain with white-yellowish spots

Could be silver, could be cobalt. It will be ore though.

Ore detector max distance

silver & gold, usually

Got a drill? Plenty of silver hunks in the dunes and at the bottom of the underwater islands. I think there's also one not that far off the shore of spoiler mountain?

If not, start looking for reefbacks.

On the walls on crevices in the seeweed forests or strewn around the great white plains with red seaweed.

Gun island is a great place for early game sandstone and shale chunks

Creepvine (kelp) forests, grassy plateaus (that's the red bits), and (carefully!) down around the thermal vents and in various deep little caves in the safe shallows. Plateaus are probably safest/easiest, although keep an eye out for some aggressive weeds. :)

The red grass area tends to have sandstone outcrops

Not sure how early you’re able to go here but sea traders dig up shale with every step, making it nearly infinite shale. Reef-backs also have barnacles on their back that contain either silver or copper