An early fifth-century cup, now in the Louvre, shows a dancing satyr.
Satyrs are horse-men, drunken, lustful, and not very smart. Satyr plays were associated with tragedy; the fourth play in a tragedian's entry at the City Dionysia was a satyr play. Only Euripides's Cyclops survives complete; there is a substantial fragment of Sophocles's Tracking Satyrs (Ichneutae), and there are smaller fragments of other plays. The story of Cyclops is adapted from Odyssey 9 and that of Tracking Satyrs from the Homeric Hymn to Hermes.
An early fifth-century cup, now in the Louvre, shows a dancing satyr.
This bowl shows satyrs and goats playing; it is at Harvard, and dates from about 500 BC.
Overview of an early fifth-century wine bowl in the Fogg Museum at Harvard. This vase shows the return of Hephaestus to Olympus, told as if from a satyr play. 
Dionysus, recognizable by his ivy wreath, leads the satyrs. 
Hephaestus rides a mule while satyrs play various instruments.
Because satyrs are slaves of Dionysus, they are often shown together with maenads. 
This vase, in Boston's Museum of Fine Arts, from about 480 BC, is an example.
This vase, from about 450 BC, shows a satyr, a maenad, and a woman; it might be a scene from a satyr play. It is in the collection of the University of Mississippi. 
The House of the Masks at Delos, dating from around 100 BC, has both satyrs and theatrical masks in its floor decorations.