The mechanism is concerted. That is, all bonds involved are formed and broken all at once. It is often referred to a remixing of molecular orbitals and the stereochemistry of more complex examples are rationalized using the sign of the molecular orbitals. There are two sigma bonds on the products side replacing 2 pi bonds on the reactants side so the reaction is favored by enthalpy. Once again, the skill you must gain is to recognize how the dienes and dienophiles fit together and how Diels-Alder adducts can be analyzed retrosynthetically to design a synthesis.
Models can be a big help in analyzing the structures of reactants and products.
Draw the product of the following reaction, the dimerization of cyclopentadiene. Or, alternatively, identify the reactants that would react to produce the following product. There are some interesting conformational, kinetic and stereochemical considerations in the reaction. The s-trans conformation would yield an impossibly strained cyclohexene with a trans double bond. Dienes that are locked in the s-cis conformation are more reactive because all are in the correct conformation.