How to resize ext3/ext4 filesystem (including root)?

The other day I had to resize (i.e. shrink) the root filesystem on one of our machines. Today a colleague wrote the following concise HOWTO for the same:

1. Reduce the size the file system on your root partition with the tool
   applicable to the file system you have on that partition, such as
   resize2fs, to a size smaller than you need.

2. Resize the partition to the desired size (it has to be bigger than the
   file system from the previous step) using a tool such as fdisk.

3. Increase the file system size to completely fill the new partition
   size (again resize2fs, depending on your file system).