How did the humans fish in the stone age?

The stone age actually covers a very wide swath of human history, not just in terms of time, but also in terms of geography. Some cultures, such as the Aztecs and the Maya had very advanced methods while still technically being in the stone age.

The question itself is actually very broad, as there were many different methods used depending on the type of fish being pursued. When pursing fish that swim close to the surface, as in the case with river fish, a spear was often used. With a certain amount of practice this could be extremely efficient. Some groups would even travel out in boats during the with large torches. These torches would lure the fish close to the surface where they could be speared or brought closer to the hooks.

Another method we would be very familiar with would be the use of hooks. Often made of bone, these hooks would have barbs carved into them, and then be placed on a line with bait. These were basically fishing rods in the modern sense.

Other methods included using sophisticated traps that allowed fish to swim in, but not allow them to swim out.

Though not technically a fish, some groups such as the Inuit even had methods for taking down a whale. They would try and get close to the animal with their boats, and then throw a harpoon connected to an air filled bladder into the whales side. When the whale tried to dive under water, it would drag around this large sac, kind of like trying to dive while wearing a life jacket. This would very quickly tire the animal out, bringing to close to the surface where it could be speared even more.

The reality is the whole issue is actually very complex, but the way people fished before the development of metals isn't really a whole lot different from how we fish today.