The key exchange algorithm is used to compute the "master secret", usually by way of computing another key known as the "pre-master secret" which is then expanded into the actual "master secret" with the PRF. DHE uses Diffie-Hellman as key exchange algorithm; ECDHE uses a variant of Diffie-Hellman that involves an elliptic curve.
In both cases, the server must send the "DH parameters" (the definition of the group in which the Diffie-Hellman will be performed -- in the case of ECDH or ECDHE, that group is an elliptic curve) and its "DH public key" (the server's half of the DH key exchange). When using DH or ECDH cipher suites, these information (group definition and server public key) are part of the server's certificate; when using DHE or ECDHE cipher suites, they are not part of the server's certificate, and are instead sent as a stand-alone
In practice, DH and ECDH are very rarely used, because certificates with DH or ECDH keys are a rarity. Instead, DHE and ECDHE are used.