Gravitational slingshot is proven to be one of the best ways to accelerate an satellite. But how does it actually help accelerating a satellite? During this process, will satellites use chemical thrusters to move out of the gravitational pull of the planet, in the vicinity of which a gravity slingshot is performed?
The hyperbola of the spacecraft past the planet trades a tiny bit of the planet's vector (from its orbital velocity) for a large boost to the spacecraft's vector; this is because the amount of energy traded is the same on both sides, but the planet's mass is millions or more times larger.
The simplest case is an approach along the line of planetary motion. If you are approaching from ahead, as you pass, you swing around (preferably in direction of rotation) the planet, and come out on a course 180° from where you started, with an increase of 2x the speed of the planet. (The planet DOES slow down, but so little that it's impossible to notice.)
Slowing can be performed as well; approach from behind, and come out 180° to the rear, and for maximum slowing, do so in a counter-rotational path. This slows you by twice the vector of the planet, accelerating the planet ever so minutely.
The pass direction needing to be in rotational direction for acceleration isn't entirely true; but is a tiny consideration. If you move in the direction of rotation, you transfer less energy to the planet in the form of rotation, as you move past less of its mass; conversely, if you go counter-rotational,you maximize interaction with the mass of the planet. Note that the effects of the planet's mass are more profound than the spacecraft's, but it all ties in, and the effect of mass passed by is signficant enough that NASA calculates for it.
Further: a ship can maximize gains by thrusting on the exit leg, from periapsis on, especially if thrusting so as to increase the radius (and decrease the drag from planetary gravity.