According to the text, Brian learned about turtles from a television program. In the story, his curiosity is piqued when he realizes that there are clawed marks on the sand going towards the lake and back towards a pile of sand further inland.
When Brian investigates by brushing aside the top pile of sand and digging down, he comes across a small chamber underground where seventeen eggs are nestling safely. He infers that the eggs must have been laid by the turtle which made the marks in the sand. Brian is fairly sure that a turtle made the marks because he remembers a television program about freshwater turtles that laid their eggs on land. Brian is extremely pleased to find the eggs as they will serve as necessary nourishment for his body.