If you use the standard Raspbian update/upgrade process (found here), this will automatically update the kernel to the latest stable version. This is the recommended procedure. However, in certain circumstances, you may wish to update to the latest 'bleeding edge' or test kernel.
The rpi-update utility will download the latest (unstable, testing) kernel version and copy all required files onto your system. Note that the latest kernel from rpi-update is not guaranteed to work correctly! Make sure that it doesn't conflict with your distribution packages. It doesn't provide a way of automatically uninstalling the files.
After upgrading the kernel, you'll have to reboot your Pi to switch to the updated version.
If you're using a compiled kernel, rpi-update will have overwritten it, and you will need to rebuild and reinstall your kernel.
Custom configurations can usually be copied over between minor kernel updates, but it's safer to use the diff utility to see what's changed and repeat your changes on the new configuration.
The Raspberry Pi Foundation kernel is part of the raspberrypi-kernel package, and the bootloader files are part of the raspberrypi-bootloader package. To revert to the current stock Raspbian kernel after trying rpi-update or a custom kernel, you need to reinstall both these packages, by running:
sudo apt-get install --reinstall raspberrypi-bootloader raspberrypi-kernel