Because they had no father, Jacob and Wilhelm grew close to each other. They attended the University of Marburg, where their law professor introduced them to philology -- the study of language in historical texts. Because of their family's poverty, Jacob and Wilhelm were excluded from the school's social life -- which drove them to pursue their studies more energetically.
After college, both brothers worked as librarians in the town of Kassel. Neither Grimm earned much at his job, but their jobs gave them enough time to continue studying, and in 1806 they began writing down the folk tales they heard around Kassel. At first, the brothers were more interested in the stories' research value than their entertainment value -- Jacob was especially concerned with how German had evolved from languages of the past, and even went on to develop "Grimm's Law," which describes how consonants changed over time to give rise to modern German.
The Grimms published the first volume of their collected folk tales -- called "Children's and Household Tales" -- in 1812, and a second volume in 1814. Though they continued to write scholarly books and articles on linguistics and medieval studies, their folk tales gained them the most recognition, and they even received honorary doctorates from their alma mater.
By the way, if you've ever read "Grimm's Fairy Tales" and felt they were a little dark for kids, you have German culture during the early 1800s to thank. After the book was published it attracted criticism for its sexual content, so the brothers edited these themes out of subsequent editions. But because the violence of the stories wasn't frowned upon in the same way, it was retained and in some cases even increased.