Does anyone have advice for getting a D&D game going for beginners that includes people who aren't familiar with RPG mechanics?

First off, I've noticed a lot of D&D chatter on here, so I figured you all would be a great resource for this. I've never played D&D but after listening to some of The Adventure Zone, I'm really getting into the idea. I want to play with a group of friends, but there are a few people who have never really played an RPG and get somewhat self-conscious playing things like board games. Any recommendations for a good starting point for this sort of situation?