I just bought a pair of Cannondale Roam shoes and Speedplay Frog pedals. When I installed the cleats on the shoes, they stick out far enough that they click on the ground when I walk. Is this the way they are supposed to be or should I do something to make them even more recessed?

That's how they are. MTB shoes have "recessed" cleats (which really just means there is a tread on the sole of the shoe that goes out as far as the cleats) while most road shoes are exposed. Have fun walking like a duck!

Well, the Roams are MTB shoes, that's why I thought maybe the cleats wouldn't stick out as far as the treads, but they do.

I think Frog cleats are somewhat thicker than SPD or Time or Crank Brothers. To completely hide the cleats, you need shoes with bigger lugs.