Short answers, pulled from the story.
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites by expelling mass in the direction opposite to travel, following Newton's third law of motion. The energy to move that reaction mass comes from chemical combustion, electrical power, or external sources such as sunlight or solar wind. The efficiency of a propulsion system is measured by specific impulse, expressed in seconds.
Chemical rockets produce high thrust over minutes by burning fuel to generate hot gas, reaching specific impulses around 300 seconds, but consume large amounts of propellant. Electric drives such as ion thrusters and Hall-effect thrusters achieve specific impulses around 3,000 seconds and can carry roughly 70 percent of a spacecraft's low-Earth-orbit mass to a deep-space destination, but produce very low thrust and require substantial electrical power.
A Hohmann transfer is the most fuel-efficient path between two circular orbits. A spacecraft fires its engine briefly to enter an elliptical orbit that touches both the origin and destination orbits, coasts in free fall, then fires again on arrival to match the destination's velocity. The technique is the standard approach for interplanetary missions.
Japan launched the IKAROS spacecraft in May 2010, which successfully demonstrated both propulsion and guidance using solar sail technology and remains active. NanoSail-D subsequently became the first solar-sail-powered satellite to orbit Earth. NASA confirmed in August 2017 that its Sunjammer solar sail project concluded in 2014, generating lessons for future sail missions.
Specific impulse measures how much change in momentum a propulsion system delivers per unit of propellant consumed. Ion propulsion engines achieve specific impulses of roughly 3,000 seconds; chemical rockets typically reach around 300 seconds. A higher specific impulse means greater efficiency and less propellant needed for a given mission.
Robert Goddard noted the possibility of electric propulsion in his personal notebook in 1906. Konstantin Tsiolkovsky published the idea in 1911. Both men preceded any practical application of the technology by decades.