Jeff touched on it, but I'll echo that a sharp razor is critical to a close shave. And, yes, 30 degrees (about 2 spine widths) is usually the best angle for shaving most of your face. But, I've also found that in tough places like your chin and neck laying the razor flatter, almost but not quite against the spine (10-20 degrees) is helpful. Otherwise the razor sometimes wants to dig in and pull in these regions, especially with tough beards. But again, sharp is imperitive. It should at least pass the hanging hair test.

Tom