Falcon 9’s first stage recovery is a beautiful maneuver in itself. Requiring three precisely timed re-entry burns to orient, control, stabilize and land the rocket successfully with precision.
Please refer to the above (beautiful) illustration to understand the Falcon 9 recovery process.
Immediately after stage separation, the Falcon 9’s first stage or booster goes through, what is called a “flip maneuver”. This is done by using cold gas thrusters located at the top of the booster. This rotates the booster by ~180 degrees and gets it oriented in the right direction for the upcoming engine burns.
Next in the sequence is Boostback burn. In this 3 of the engines are ignited for a few seconds and the booster trajectory is reversed. Usually, the booster reaches up to a height of ~200 km before ascending down. The descent happens a few seconds after the boostback burn.
After this, the booster descends for a few more seconds and soon is followed by “Entry burn”, in which 3 engines ignite again to slow down the speed of the booster. This happens at a height of ~ 55 km
Finally, just a few meters away from landing the final “landing burn” is executed using only one of the Merlin engines. Keep in mind that throughout the journey grid fins are deployed that continuously control and orient the booster through minute changes in its aerodynamic behavior.
Typically 6-10% of the total fuel mass is required for executing all three re-entry burns. If the landing is occurring offshore, then the fuel needed is ~6%. In case, the 1st stage has to be taken to the launch site, then ~10% of the total fuel is used.