vertices, propagators, and external legs

Every Feynman diagram, no matter how complicated, is built from just three kinds of piece, the way every sentence is built from words. Once you can name these three pieces, you can read almost any diagram. They are the external legs (the lines that stick out at the edges), the vertices (the points where lines meet), and the propagators (the internal lines that connect one vertex to another). Think of vertices as the events, propagators as the bridges between events, and external legs as the particles you actually start with and end up with.

Each piece has a precise job in the calculation. An external leg is a real particle entering or leaving the process — the electrons in the beam, the photon flying off into a detector. A vertex is a single interaction: one place where, say, an electron emits a photon. The strength of that interaction is set by the coupling, so each vertex contributes a factor of the coupling to the answer. A propagator is the internal go-between, a virtual particle carrying energy and momentum from one vertex to the next; mathematically it contributes a factor that grows when the virtual particle is close to being a real, on-shell particle. Multiply the factors for all legs, vertices, and propagators, and you get that diagram's contribution.

This Lego-like structure is why Feynman's method is so powerful: the same handful of rules (one per type of vertex, one per type of propagator) lets you assemble and compute any process in a theory. In quantum electrodynamics there is essentially one vertex — an electron, a positron, and a photon meeting at a point — and from that single building block you can draw every electromagnetic process there is. A subtlety worth keeping straight: external legs are real, observable particles, while propagators are virtual and never directly seen.