Scheele achieved astonishingly prolific and important results without the expensive laboratory equipment to which his Parisian contemporary Antoine Lavoisier was accustomed.  Through the studies of Lavoisier, Priestley, Scheele, and others, chemistry was made a standardized field with consistent procedures. Although Scheele was unable to grasp the significance of his discovery of the substance that Lavoisier later named oxygen, his work was essential for the abandonment of the long-held theory of phlogiston.
Scheeles study of the gas not yet named oxygen was prompted by a complaint by Torbern Olof Bergman, a professor at Uppsala University who would eventually become Scheeles friend. Bergman informed Scheele that the saltpeter he had purchased from Scheeles employer, after long heating, produced red vapors (now known to be nitrogen dioxide) when it came into contact with acetic acid. Scheeles quick explanation was that the saltpeter had absorbed phlogiston with the heat (had been reduced to nitrite, in modern terms) and gave off a new phlogisticated gas as an active principle when combined with an acid (even a weak acid).
Bergman next suggested that Scheele analyze the properties of manganese(IV) oxide.  It was through his studies of manganese(IV) oxide that Scheele developed his concept of "fire air" (his name for oxygen). He ultimately obtained oxygen by heating mercuric oxide, silver carbonate, magnesium nitrate, and other nitrate salts. Scheele wrote about his findings to Lavoisier who was able to see the significance of the results.  His discovery of oxygen (ca. 1771) was chronologically earlier than the corresponding work of Priestley and Lavoisier, but he did not publish this discovery until 1777, after both of his rivals had published.
Although Scheele would always believe in some form of the phlogiston theory, his work reduced phlogiston to an unusually simple form, complicated only by the fact that chemists of Scheele's day still believed that light and heat were elements and were to be found in combination with them. Thus, Scheele assumed that hydrogen was composed of phlogiston (a reducing principle lost when objects were burned) plus heat. Scheele speculated that his fire air or oxygen (which he found the active part of air, estimating it to compose one quarter of air) combined with the phlogiston in objects to produce either light or heat (light and heat were presumed to be composed of differing proportions of phlogiston and oxygen).
When other chemists later showed water is produced when burning hydrogen and that rusting of metals added weight to them and that passing water over hot iron gave hydrogen, Scheele modified his theory to suggest that oxygen was the salt (or "saline principle" of water), and that when added to iron, water was reproduced, which added weight to the iron as rust.