I have yet to find a better article than this one on transitioning from Waterfall to Agile.
Transitioning From Waterfall to Agile
Agile is designed to promote positive and functioning relationships among team members, enabling self-administered teams and team processes that address the continual consumer demand for updates and the fluctuating levels of software consumption. Teams integrate multi-talented resources into cross-functional process to boost production and inspire innovation.
Agile methodologies allow assessment of project direction throughout the entire software lifecycle. The strategy of regular iterations incentivize teams to produce potentially shippable output at the end of each incremental build, providing immediate opportunities to redirect objectives for quicker and more continuous delivery. In this way, software development can happen while requirements and analysis are occurring. Development is integrated into fact-finding through the build activity rather than strictly defined as stages of production.
Continue reading here.