I treat my EU's like I do every single outboard motor that I've owned.
Shut the fuel petcock off. Drain the carb. Close the screw up on the float bowl so it's ready to go in the event of an emergency. Choke the motor. Pull the starter cord 3x briskly with the motor in the "off" position, to suck any residual fuel out of the jets. Store.
On a Honda, turn on the petcock/start switch and wait a few minutes before just pulling the starter through gently 15-20 times. You'll know if you pull it slow and it pops, it's time to lay into the starter then, should fire the motor right up with a little more vigorous pulling. Turn the choke setting to 1/2 way, run 30 secs to a minute, turn choke off fully.
