The labor theory of value is used with respect to production for exchange. Before capitalism, production for use, direct use of products by their producers, is the predominant form of economy. Except for the surpluses taken by force for the ruling classes, peasants in precapitalist societies "owned" most of what they produced because they used and consumed it. They possessed it ( ninetenths of the law ?)
It is only with the wagelabor-capital relationship coming to predominate in an economy that most production is for exchange, i.e. production of commodities predominates, not for direct use by the producer.
The commodity producer _sells_ her labor power to the capitalist. The capitalist also owns and supplies raw materials and instruments of production which add value to the product. So, the worker doesn't own those ingredients of the product, and doesn't gain property in that product. The worker only owns her labor power, and sells that. That's what defines a wagelabor-capitalist relationship. Anyway, it can be seen how by this reasoning the worker doesn't own the commodities she produces with her labor.
Marx's idea is that labor power is the only source of _new_ exchange value in the process, because labor power has the unique quality of being able to add more value to a product than the value of the labor that went into reproducing that labor power. This is the "secret" of surplus value, or some such.
The capitalist exploits this surplus value produced by the extra time worked, beyond the time worked that has the value of the commodities by which the labor power is reproduced.
Charles