A Body is a point in space.
A Shape makes up the second dimension in the form of a polygon.
A Fixture attaches a Body and a Shape together.
In the newest version (3.3.1) of FPE, the BodyFactory creates a body and attaches a shape to it for you. To access the fixture on the body, you simply access Body.FixtureList.
Collisions are automatically calculated when a shape is attached to a body. If you need to know when the body collides with other bodies, you can subscribe to each fixture using the Fixture.OnCollision delegate. Example:
Body.FixtureList.OnCollision += MyCollisionHandler;