You'll need all three words of the Bend Will shout to be able to tame dragons, but the good news is that you'll obtain them all as part of Dragonborn's main questline. Once you have them, you can fast travel around Skyrim to the various dragon locations on your map and simply use it 5 times.
To tame a dragon, use the full shout on it when it gets close. It will land nearby, and if you approach it you'll be prompted to press A to mount it. Do this and enjoy the view a bit, then press A again to have the dragon land so you can move on to the next one.
Note: This must be done on 5 different dragons! It doesn't count towards the achievement if you wait for the same dragon to become hostile again and then tame it again. (Thanks ponypo2001 for reminding me.)