Charley is right as regarding private lands, in most states, but one should check state laws. Also, one should be aware if they are on public land or private.
So, if you are interested in buying old Indian relics, it is in your best interest to ensure where they were found.
About 60 years or so ago a bunch of kids over in East Texas asked a farmer if they could 'hunt for buried treasure' on his property. He gave them the go-ahead, they went out--& actually found a cache of money. It amounted to a fair sum for the day--at least a couple of hundred dollars. The farmer stepped in & claimed it. The kids' parents sued. The court ruled that, since he had not been present when the money was found, he had given the kids permission to look for buried treasure, & in giving them permission to 'hunt buried treasure' on his property he had not specified that he would have an interest in their find if they found anything, he had no legal claim to the money.
I used to hunt 'picture agate' for an artist. When I made my research forays into the Texas hill country, I'd tell anyone on whose property I went that I was looking for picture agate & if I found anything else of value I'd bring it to them to see if they wanted it. The artist charged me $5 a stone to cut the stone in half, but if it had a usable inner 'picture' he'd pay me a dollar a pound for the stone. Most of the stones weighed 20 to 30 lbs & abt 9 out of 10 had a 'picture,' so that made my gas money. I found a lot of old metal--tools & such--& one artifact I wanted to take home but had no way to take it. It was the body & windshield frame of abt a 1922 Model T Ford roadster.