But how is a piece of land (for example) originally claimed?

The first step in that process is the individual's expression of a value preference - that is, he selects a particular piece or amount of land, rather than continuing to look for another piece of land somewhere else.

Having made this value judgement, he proceeds to bound the land, running a fence or placing recognizable markers indicating the extent of his claim.

He will also generally file and make a public (government) record of these boundaries.  He will do this because he wants others to respect his boundaries.

In order to have others respect his boundaries, he must be prepared to similarly respect the boundaries of others.  It is generally far less expensive and more practical to respect the boundaries of others and to make public notice of his own boundaries, than to overlook such formalities.

These days, since almost everything is already owned, we tend to file such records in county courthouses and records bureaus, in order to provide "notice" to our neighbors that we own this-or-that parcel of land.

Even before there were county courthouses however, or even bureaucratic governments as we know them now, men owned (and not merely possessed) land.