The discovery of oxygen happened in the 1770s, not the 1850s. It is normally credited to Joseph Priestley (1733–1804), an English clergyman and self-taught chemist. In those days chemistry was more like alchemy, or it was called apothecary. Nobody really knew what anything was made of. They thought everything was made of air, earth, water, and fire. There was no such thing as the periodic table of elements. The concept of "elements" was still evolving. Same with the idea of a gas. In 1774, during an experiment, Priestley noticed that mercuric oxide (they used to call it "mercury calx") when heated, yielded a "special air" that made a candle burn much faster, and that it would support respiration or life. He put a mouse in a vessel with his "special air" and it lived four times longer than with regular air, and was revived afterwards. Priestley published these experiments and observations in 1774.
A couple years before, in 1772 Karl W. Scheele, a Swedish apothecary discovered oxygen in a similar way, but never published his findings until 1777.
It was shortly after Priestley's discovery that he went on a trip to France and met Antoine Lavoisier, a French lawyer who was conducting scientific experiments trying to figure out what air was made of. Priestley told Lavoisier of his experiments, and this was the key Lavoisier needed to make sense of his own findings that ordinary air was made up of two major components in a ratio of about 3 to 1. Lavoiser named Priestley's special air “oxygen,” which comes from the Greek word roots that mean “acid-former.”
In summary, oxygen was probably first discovered by Scheele, but first reported by Priestley. It was not named until a bit later by the Frenchman Lavoisier. Who should get the credit?
A good explanation of the story is available at the website of the American Chemical Society although they focus on Priestley as he eventually moved to the United States and became an American.