Their legs are higly sensitive to vibrations sent out by floating insects, especially those in distress. The spider will rapidly approach the prey, inject it with venom, then drag the unfortunate to shore, where it can be consumed without danger from other (underwater) predators. They have also been known to dangle a leg under the water surface in order to attract small fish, which they then capture by making a sudden plunge, holding the fish in the powerful legs while subduing it with venom. Fish are also dragged bodily to bankside to be consumed.

One species of fishing spider in South America actually constructs funnel-shaped webs between stones at the water's edge, then drives tadpoles into the funnel trap where they can be eaten. 

This fishing spider is 60mm (2 1/2") across the longest legs