Skateboards are made up of three components: the skate deck, trucks and wheels. Skateboard trucks are made out of metal and are very durable, often lasting for years until they are ground beyond use or break (in very rare cases). A truck set-up consists of a base plate, upon which a hanger and axle are held into place with a kingpin. Rubber bushings are used as shocks and are set around the kingpin. Like all shocks, bushings wear out and occasionally need to be replaced.
Loosen the bolt on your skateboard trucks. Bushings are made of rubber and are extremely stiff when they are new. When you reassemble your trucks with the new bushings, do not tighten the bolt completely. This will give you some wiggle room to work with while the bushings gain their shape and soften.
Ride your board to break in the bushings. You are ready to skate once your bushings are set on the trucks, but it is recommended you "cruise around" for your first skate session. As you get a feel for the new bushings, you will notice stiffness and awkwardness at first, but it will go away in a couple of days. Spend your first few skate sessions either skating on flat ground or basic riding in a mini ramp.
Adjust the trucks after a few days of breaking in the new bushings. As soon as your board starts to feel normal---no tightness or awkward pulling off to one side---tighten the trucks as you would normally ride them. The bushings are now broken in and you are ready to get back to some shredding.