The interview process was straightforward, much the same, if not a tad less competitive than for similar positions at Ivy League schools (I interviewed and obtained a job at Yale as well). If you're sharp, and present yourself well, you'll get in. You have to be teachable for this job. Communicate that, somehow. If you lack experience, don't try to schmooze your way around that. There are plenty of labs around campus that can give you the experience you need. Don't make up anything/stretch things, and you'll do well. You'll be in there working with very bright/capable graduate students and post-docs. Look the part, act the part.

I met with the lab's PI in two occasions to discuss several matters related to the position and my competitiveness. It was an overall nice experience, as the PI was a very nice and passionate scientist, so he was mainly looking for someone who would fit in his lab and also showed a passion for research.