how can I smoothly move a camera without a dolly?
You want something like a Steadicam.

The idea is to add weight to the camera assembly so that it is stabilized by an increase of moment of inertia. For larger rigs, the entire thing might be supported by the cameraperson's body on a harness.

For smaller applications, the mount point of the camera is right above where you grip the assembly, and the pivot point is at the top of this grip. Then, a rigid strut extends from the mount point to below the grip, and weight is added at the bottom of this strut so that the center of gravity of the entire assembly (camera included) is at the pivot point.

This is an example of something like this that you can purchase, but if you're on a tight budget you might even be able to make something yourself.