The Flying Things adds magic carpets and brooms to Minecraft.
These are moderately easy to craft for some of the carpets you need a Heart of the Sea, carpets and soul sand. A Heart of the Sea can be found in treasure chests that you can find using a treasure map found in shipwrecks.
For others you will need a Phial of Animation which can be obtained by generated chests or by killing a Wither.
All you have to do is hold ‘W’ and look in the direction you want to go and off you go through the air. But be careful, it will break leaves as you go through them.