There are a number of things that people enjoy about strategy/corporate development, namely making potentially impactful decisions on an organization in terms of organic growth or acquisitions while also leading more of a sane lifestyle. I have several friends that transitioned from finance or consulting into corporate development. The finance guys say they like corporate development because of the better work-life balance and also working with the same “client” all the time (i.e. the organization that they work with). The two girls from consulting I know that moved to corporate development also said they enjoyed the better lifestyle, as well as the fact that they could potentially implement their ideas (as opposed to just making recommendations to clients and moving on).
In the better economic times (2005-2007), people were able to make the transitions right out of their undergrad experience by way of personal networks or placements from their seniors, i.e. an engagement manager at McKinsey might recommend to one of their client organizations that they should hire you. There’s still some of that going on, but by and large the best avenue of getting into corporate development is through business school simply because so many firms come to recruit on campus. Aside from that, working your own personal networks is as good a bet as any. Corporate development employment opportunities do occasionally go through recruiters, but typically only for pretty senior hires. It’s really more about using your own personal networks (either professionally or through undergrad/MBA) or LinkedIn, in my view.