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A face of a polyhedron is one of the flat surfaces. These are two dimensional objects. Two faces meet at an edge, which is a line - a one dimensional object. Three or more edges meet at a vertex which is a point. A point has no dimensions.
When two sides (called faces) of a 3-dimensional shape meet, they meet at an edge.
An edge is where two faces of a three dimensional figure meet. An vertex is where three edges meet.
They are the points where three (or more) planes (or faces of the shape) meet.
A side and face of a three-dimensional object are the same thing. A pyramid is a generic term. It refers to a solid object with a polygonal face - with n number of sides (n > 2) - and n triangular faces that meet at an apex. So a pyramid can have 4 or more faces.