I visited the Exeter Library two years ago. Actually slept over night in my car in the parking lot because I didn't have money for a hotel. It's a pretty powerful building. The design is made from a series of concentric squares. The process? It's as different as each individual building and each individual architect. Ideally, there wouldn't be one starting point, but many co-existing starting points. To say that an architect works from the inside out or vice versa is too reductionist. One might typically start with a request of types of spaces needed, called the program. In the case of the Exeter, maybe a lobby, reception, reading kiosks, book stacks, etc. You can see some of his earlier sketches of these relationships here in the lower left http://jtpennington.com/italy/wp-content/uploads/2008/11/lib.... You can see him working out ideas in plan and elevation. Although he primarily works in plan (Le Corbusier famously said 'the plan is the ultimate generator') At the same time though, one should be thinking about procession, meaning how and when do we first arrive to view the building - walking to it from across the street, driving to the parking lot etc. then entering the building, seeing the lobby,and finally, maybe searching for a book on the fourth floor or something. This is all called the architectural 'promenade'. The architect at his/her fullest potential designs these environments - high low loud quiet light dark hard soft public private. The way the spaces work together, cohesively, often takes some massaging. Kahn was known for thinking of buildings in terms of serving and served spaces. The stair well is a serving space, the reading room is a served space. The janitors closet is a serving space, the covered entry is a served space. Really though there are a million ways to approach the design of a building - economic, environmental, political, functional, structural....