It doesn't matter ... ;-) Every land has an owner and it is polite to agree on the search conditions in advance. It is reasonable to find out in advance in the local museum of archeology (if such exists). In any case, you must not damage anything on the land (digging in an unharvested field is a perversion, for example) - so whatever you do on the land, restore it to its original state (throwing holes ...). If the landowner does not agree with the search, it is his decision and you should respect it. At archaeological sites, any search (without permission and - better, the presence of archaeologists) is prohibited. If you find something, carefully document everything (take a picture, determine the location) and publish it (for example, in cooperation with the already mentioned museum). If you find something bigger, call in experts.