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.
Do not use rpi-update unless you have been recommended to do so by a Raspberry Pi engineer. This is because it updates the Linux kernel and Raspberry Pi firmware to the very latest version which is currently under test. It may therefore make your Pi unstable, or cause random breakage.
To use rpi-update, execute it using sudo as follows:
sudo rpi-update
The rpi-update utility will download the Linux kernel and Raspberry Pi firmware that are currently being tested and install them onto your Pi. Note that rpi-update does not provide a way to revert the changes that it makes to your system.
After upgrading the kernel, you must reboot your Pi to switch to the updated version.
If you're using a compiled kernel, rpi-update will overwrite 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 supplied by the raspberrypi-kernel package, and the bootloader and firmware are supplied by 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 as follows:
sudo apt update
sudo apt install --reinstall raspberrypi-bootloader raspberrypi-kernel
Note that this will install the latest stable versions of the kernel, bootloader and firmware that are available from the package repository, which may not be the same versions that you were running before you ran rpi-update.