Usage
Simply rightclick to launch yourself. Direction is similar to the "Slimesling" from Minecraft's Tinker's Construct mod (opposite your facing direction). Leftclicking will change the sling's power, and shift-leftclicking will display the sling's power HUD element. Pressing shift mid-flight will cancel your current trajectory, allowing you to sling again!
Crafting
Minetest_Game
Make a "Y" pattern of dirt_with_grass nodes on a 3x3 crafting grid and place a bucket of water in the top-middle
Nodecore
Pummel a wet sponge and dirt together with your strongest mallet.
High-Flying Fun
I am not familiar with the aforementioned Slimesling mod this is adapting, but found it fun, interesting, and well balanced.
As far as a practical form of transportation goes, I haven't exactly figured that out yet, but in theory, one could setup a series of stations for "refueling" by crafting more replacement mudslings to continue a long journey. Getting the trajectory right, and not having problems with hitting an unloaded mapblock boundary, might be challenges. It would be interesting to see someone make something interesting like a travel network based on this.
boing
"I believe I can fly........" fun to use.