From 1847 to 1848, Čermák studied at the Academy of Fine Arts in Prague as a pupil of Christian Ruben.
Many of his paintings are in the collection of the National in Prague. His birth house at Betlémské náměstí 10 (Betlémské Square Number 10) has since been decorated with a commemorative statue of a girl crowned with laurel and with a golden inscription of his surname. As a child, Čermák suffered an injury of the hip, and due to subsequent complications he spent a part of his childhood strapped to the bed in a narrow chest.
This accident apparently inspired his artistic beginnings, as while in bed, deprived of the possibility of moving, he found an interest in drawing.
His family was involved in arts patronage. His mother supported anonymously the renowned Czechoslovakian writer Božena Němcová.
lieutenant was Čermák"s desire to be a history painter. As he felt that the training in Prague would be insufficient, he traveled to Antwerp, where he studied with Gustave Wappers and Louis Gallait.
In 1852 he settled in Paris.
However, he travelled widely through Europe and often returned to his homeland. He frequently visited Montenegro, and in 1862 he fought alongside local soldiers in their clashes with Ottoman troops at the battle of Cetinje. One of the streets in Podgorica was named after him.
In 1874 he designed and built his own house in Paris.
He died in 1878 in Paris. His remains were transferred to Prague in 1888.
He is buried at Olšany Cemetery in Prague.