You can find a good summary in Avot D'Rav Nattan ch 6, mishnah 2.
Summarizing some of the story cited there:
He was a shepherd and began learning at 40 years old. Once he passed by a well and noticed a carved stone. He asked who carved this stone, and they told him that it was the water that constantly dripped on it. From this, he said that if water was able to carve a hole in the hard rock, surely the words of Torah could carve his heart.
Immediately, he and his son went to learn at a childrens teacher. He asked the teacher to teach him the Aleph Bet. Eventually, he learned the entir Torah.
Then, he went to learn before R. Eliezer and R. Yehoshua asking them to teach him Mishnah. When they taught him, he would ask, "Why is the letter Aleph written this way, and Bet written this way?" They pushed him aside (because they thaught that he wasn't focusing). However, because Rav Akivah was so curious and exacting on seemingly small details, he developed the unusual talent of revealing and explaining deep secrets that no one else was able to.
Personal note: To me Rav Akivah is a prime example of the adage in Pirkei Avot 4:3:
[Ben Azai] would say: Do not disparage anyone, and do not shun any thing. For you have no man who does not have [his] hour, and you have no thing which does not have a place.