Getting a job at a consultancy

I’m third year law student who’s going into business law and would like to have some experience in business consulting. I want to get a summer job at a consultancy. I’d like to know more about the sort of selection that’s done and what to put emphasis on.
A bit about me: I’m in my late 20s but look in my early 30s in a suit (the shaved head does that). I took some management courses where I consistently did very well and like to believe I have a good grasp of economics. I’ve been reading the magazine The economist since I was 16/17. My undergraduate degree was in philosophy and anthropology. My main job so far was as an enlisted reservist for two years. I’ve done a fair amount of volunteering (boy scouts, community center, a centrist political party, student legal clinic). My personality type is INTJ.
So, anyone have information to contribute about just what is done in a consultancy, the selection process and what I should emphasise in the cover letter and interview?