Define the rules up front and post them in writing at the front of the class. Even if all of the class is not reading yet, the poster reminds them there are rules, and the poster gives you a visual aid to remind them of the expectations. Keep the rules simple and limit them to 10. Include when the students must be quiet and what your cue will be when you need them to be quiet. Consistently enforce the rules.
Avoid dead time. Even a group of adults has a hard time sitting quietly when they have nothing to do. Plan activities that the students can do in silence while others finish up their individual assignments. For example, keep coloring sheets available or a stack of picture books. Use movement to give the kids a chance to get out of their seats and expend pent up energy. Dividing your class into work centers allows children to move from one area to the next. Make a game of it and have the kids walk once around the room between each new assignment.
Kindergarten children have short attention spans, particularly if something more interesting is going on. Provide reminders that they can associate with quiet time. The ringing of a bell, the click of a clicker or perhaps a hand signal. Avoid raising your voice to regain control of your classroom. You will likely go home hoarse if you do, and the children will likely get louder to hear each other over you. Speak directly to one of the worst offenders, at eye level, in a normal voice. Speaking at his level takes away the edge of threat and will gain his attention quicker than yelling at him from across the room. Once children see how you handle him, they will likely quiet down, if for no other reason than to hear what you are saying.