UGH SO MUCH BAD ADVICE.
Emily, please listen to Brendan and Seth (who are apparently the only people who ride mopeds). Don't listen to anyone else. DON'T ride diagonally across the grates. don't put your feet down. two wheeled vehicles balance at speed. the moped will feel a little strange, like when you drive across white painted lines in the road - just a little less traction then you're used to.
There's like a specific section about this in the DMV motorcycle handbook (in CA at least.) Read up people.