Do you mean: "I ran onto the beach and STARED at the sea"? (To stare)

It's hard to tell without context - there are two equally possible but very different meanings here. If the next sentence is "I couldn't swim...", then "started" means "(I) jumped a little, in shock/surprise".

To: Roland and Peachey: I was able to find the quotation in Google "books." Yes, the word IS "stared." In his book "Screw it, Let's do it: Lessons in Life," Sir Richard Branson writes: "When we got here, I ran onto the beach and STARED at the sea. I longed to swim, but I had never learned how to." (Page 68)