There are two types of brake boosters: vacuum and hydraulic. The most common used is the vacuum brake booster which uses engine vacuum to add force onto of the pressure being applied to the master cylinder. Usually either an oil leak from the master cylinder or age of the brake booster cause it to fail. Once it fails, a brake booster replacement is necessary.
When a technician is replacing a brake booster, they first drain the master cylinder of all brake fluid. Then the master cylinder is removed and the brake booster vacuum hose, if applicable, is disconnected. The defective brake booster is removed and the new one is installed. The technician re-installs the brake master cylinder, connects the vacuum hose, and bleeds the entire brake system. Finally, the vehicle is test driven to make sure the repair was successful.
Most manufacturers will cover the cost of a brake booster replacement under the bumper-to-bumper warranty section of the factory warranty. There are extended auto warranties available that will cover the cost of replacing the brake booster under certain levels of coverage.