The reason tires need to be rotated is to make them last longer by making them wear more evenly. Each tire position on a given car will wear out at different rates depending on the car’s design, tire construction and your driving habits.
Typically the tires on a car’s driven wheels will wear out faster than the others. Cars that are front wheel drive typically wear the front tires faster, whereas cars that are rear wheel drive tend to do so with the rears. Also, there could be uneven wear from side-to-side which could occur for any number of reasons including driving on crowned roads, alignment issues and so on.
These all impact tire wear and how often they should be rotated.
Some cars I never bother to rotate, while others seem to require frequent rotation (which to me is every 15k miles or so). The owner’s manual will usually have a recommended interval as part of the maintenance schedule, and the tire rotation pattern. Sometimes it will also have the torque requirements. If the owner’s manual doesn’t have it, a service manual will.
Note that not all cars can have their tires rotated. For example if wheel/tire sizes are different front and rear, or if the tires are unidirectional then this does not apply.
At a bare minimum you need a jack and wheel chock, lug wrench, torque wrench and spare wheel/tire. If you have four jack stands it will save a lot of work because you’ll be able to get all the wheels off the car at the same time, and won’t need the spare.
In a pinch you can use the jack that came with the car, as well as the lug wrench but I would suggest using a floor jack where possible.